4.4 Compound Angle Formulas

📖 Chapter 4 Trigonometry
📄 Page 228
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TrigCh5.1lectureTube

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000. Section Intro

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002. Evaluating Cos 75 in Exact Values

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003. Evaluating Cos 15 in Exact Values

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004. Simplifying Trig Expression using Sine Formula

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005. Simplifying Trig Expression using Cosine Formula

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006. Proving Cosine Co-functional Identities with Compounded Angle Formulas

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007. Proving Identities with Tangent Compounded Angle Formula

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008. Identity of Differential Quotient using Sine Compounded Angle Formulas

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009. Find sinA+B from given ratios ex1

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011. Finding the location of 2x angle given single x

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012. Finding double of x ratios given single x ratios

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TrigCh5.1lectureproofsTube

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001. Proof of Compounded Angle Formula using Unit Circle for Cosine Ratio

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003. Proof of Sine Compounded Angle Formula using the Cosine Formula

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004. Proof of Tangent Compounded Angle Formulas

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yt.import.sol.704

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1

001. Q1a

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Answer
📚 Related Lectures
12.3.2 AdvFun, Trigonometry, Sum Formula, compress to simplify
🎓 002. Compress Cos
🎓 001. Compressing Sine
⏱️ 0:340🎬 EAxSZLG_KZo
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001. Q1b

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Answer
📚 Related Lectures
12.3.2 AdvFun, Trigonometry, Sum Formula, compress to simplify
🎓 002. Compress Cos
🎓 001. Compressing Sine
⏱️ 0:261🎬 FYpr_lXP8nQ
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001. Q1c

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Answer
📚 Related Lectures
12.3.2 AdvFun, Trigonometry, Sum Formula, compress to simplify
🎓 002. Compress Cos
🎓 001. Compressing Sine
⏱️ 0:261🎬 xdClC2EtfGA
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001. Q1d

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Answer
📚 Related Lectures
12.3.2 AdvFun, Trigonometry, Sum Formula, compress to simplify
🎓 002. Compress Cos
🎓 001. Compressing Sine
⏱️ 0:230🎬 kWhF5OgoobE
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002. Q2a

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Answer
📚 Related Lectures
12.3.2 AdvFun, Trigonometry, Sum Formula, compress to simplify
🎓 002. Compress Cos
🎓 001. Compressing Sine
⏱️ 0:550🎬 qPMgEbW_XYY
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002. Q2b

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Answer
📚 Related Lectures
12.3.2 AdvFun, Trigonometry, Sum Formula, compress to simplify
🎓 002. Compress Cos
🎓 001. Compressing Sine
⏱️ 0:510🎬 FTHzf2IfaQs
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002. Q2c

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Answer
📚 Related Lectures
12.3.2 AdvFun, Trigonometry, Sum Formula, compress to simplify
🎓 002. Compress Cos
🎓 001. Compressing Sine
⏱️ 0:360🎬 N3uSCf4IRmo
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002. Q2d

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Answer
📚 Related Lectures
12.3.2 AdvFun, Trigonometry, Sum Formula, compress to simplify
🎓 002. Compress Cos
🎓 001. Compressing Sine
⏱️ 0:471🎬 zfFo_qD-Lc8
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003. Q3a

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Answer
📚 Related Lectures
12.3.2 ADVFUN, TRIG, SUM FORMULA, given.Sin.Cos, expand.evaluate
🎓 001. Section Intro
🎓 003. Exact Value with Sine Sum Formula
🎓 002. Exact Value with Cos Sum Formula
⏱️ 0:441🎬 HhXmfRyBPS0
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003. Q3b

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Answer
📚 Related Lectures
12.3.2 ADVFUN, TRIG, SUM FORMULA, given.Sin.Cos, expand.evaluate
🎓 001. Section Intro
🎓 003. Exact Value with Sine Sum Formula
🎓 002. Exact Value with Cos Sum Formula
⏱️ 0:390🎬 HTWj7GW-p98
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003. Q3c

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Answer
📚 Related Lectures
12.3.2 ADVFUN, TRIG, SUM FORMULA, given.Sin.Cos, expand.evaluate
🎓 001. Section Intro
🎓 003. Exact Value with Sine Sum Formula
🎓 002. Exact Value with Cos Sum Formula
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003. Q3d

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Answer
📚 Related Lectures
12.3.2 ADVFUN, TRIG, SUM FORMULA, given.Sin.Cos, expand.evaluate
🎓 001. Section Intro
🎓 003. Exact Value with Sine Sum Formula
🎓 002. Exact Value with Cos Sum Formula
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004. Q4a

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Answer
📚 Related Lectures
12.3.2 ADVFUN, TRIG, SUM FORMULA, given.Sin.Cos, expand.evaluate
🎓 001. Section Intro
🎓 003. Exact Value with Sine Sum Formula
🎓 002. Exact Value with Cos Sum Formula
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004. Q4b

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Answer
📚 Related Lectures
12.3.2 ADVFUN, TRIG, SUM FORMULA, given.Sin.Cos, expand.evaluate
🎓 001. Section Intro
🎓 003. Exact Value with Sine Sum Formula
🎓 002. Exact Value with Cos Sum Formula
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005. Q5a

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Answer
📚 Related Lectures
12.3.2 ADVFUN, TRIG, SUM FORMULA, given.Sin.Cos, expand.evaluate
🎓 001. Section Intro
🎓 003. Exact Value with Sine Sum Formula
🎓 002. Exact Value with Cos Sum Formula
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005. Q5b

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Answer
📚 Related Lectures
12.3.2 ADVFUN, TRIG, SUM FORMULA, given.Sin.Cos, expand.evaluate
🎓 001. Section Intro
🎓 003. Exact Value with Sine Sum Formula
🎓 002. Exact Value with Cos Sum Formula
⏱️ 0:471🎬 XQX85eODKfk
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006. Q6a

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Answer
📚 Related Lectures
12.3.2 ADVFUN, TRIG, SUM FORMULA, given.Sin.Cos, expand.evaluate
🎓 001. Section Intro
🎓 003. Exact Value with Sine Sum Formula
🎓 002. Exact Value with Cos Sum Formula
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006. Q6b

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Answer
📚 Related Lectures
12.3.2 ADVFUN, TRIG, SUM FORMULA, given.Sin.Cos, expand.evaluate
🎓 001. Section Intro
🎓 003. Exact Value with Sine Sum Formula
🎓 002. Exact Value with Cos Sum Formula
⏱️ 1:350🎬 WNAeXw5dJak
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007. Q7a

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Answer
📚 Related Lectures
12.3.2 ADVFUN, TRIG, SUM FORMULA, given.Sin.Cos, expand.evaluate
🎓 001. Section Intro
🎓 003. Exact Value with Sine Sum Formula
🎓 002. Exact Value with Cos Sum Formula
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007. Q7b

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Answer
📚 Related Lectures
12.3.2 ADVFUN, TRIG, SUM FORMULA, given.Sin.Cos, expand.evaluate
🎓 001. Section Intro
🎓 003. Exact Value with Sine Sum Formula
🎓 002. Exact Value with Cos Sum Formula
⏱️ 1:201🎬 NpFXns-b3Lg
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21

008. Q8a

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Answer
📚 Related Lectures
11.3.2 RELATIVE ACUTE ANGLES, given.Ratio.Quadrant, find.other.ratios
🎓 001. Given Ratio and Quad, find other ratios
⏱️ 0:330🎬 UwPdaNVVdCY
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008. Q8b

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Answer
📚 Related Lectures
11.3.2 RELATIVE ACUTE ANGLES, given.two.ratio, find.quadrant.ratios
🎓 001. Given ratio and one more ratio sign, find Quadrant the angle is in
⏱️ 0:301🎬 pg2w-Qei2AA
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009. Q9a

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Answer
📚 Related Lectures
12.3.2 ADVFUN, TRIG, SUM FORMULA, given.Sin.Cos, expand.evaluate
🎓 001. Section Intro
🎓 003. Exact Value with Sine Sum Formula
🎓 002. Exact Value with Cos Sum Formula
⏱️ 0:450🎬 gC4h2uVzwMI
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009. Q9b

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Answer
📚 Related Lectures
12.3.2 ADVFUN, TRIG, SUM FORMULA, given.Sin.Cos, expand.evaluate
🎓 001. Section Intro
🎓 003. Exact Value with Sine Sum Formula
🎓 002. Exact Value with Cos Sum Formula
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009. Q9c

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Answer
📚 Related Lectures
12.3.2 ADVFUN, TRIG, SUM FORMULA, given.Sin.Cos, expand.evaluate
🎓 001. Section Intro
🎓 003. Exact Value with Sine Sum Formula
🎓 002. Exact Value with Cos Sum Formula
⏱️ 0:580🎬 iJPX4byBSpM
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26

009. Q9d

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Answer
📚 Related Lectures
12.3.2 ADVFUN, TRIG, SUM FORMULA, given.Sin.Cos, expand.evaluate
🎓 001. Section Intro
🎓 003. Exact Value with Sine Sum Formula
🎓 002. Exact Value with Cos Sum Formula
⏱️ 0:201🎬 iWY-7gBgmOI
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27

010. Q10a

Question
Answer
📚 Related Lectures
11.3.2 RELATIVE ACUTE ANGLES, given.two.ratio, find.quadrant.ratios
🎓 001. Given ratio and one more ratio sign, find Quadrant the angle is in
⏱️ 1:110🎬 7ltN9m1-5-8
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28

010. Q10b

Question
Answer
📚 Related Lectures
11.3.2 RELATIVE ACUTE ANGLES, given.Ratio.Quadrant, find.other.ratios
🎓 001. Given Ratio and Quad, find other ratios
⏱️ 2:010🎬 LYJDsRN8AVk
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011. Q11a

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Answer
📚 Related Lectures
12.3.2 ADVFUN, TRIG, SUM FORMULA, given.Sin.Cos, expand.evaluate
🎓 001. Section Intro
🎓 003. Exact Value with Sine Sum Formula
🎓 002. Exact Value with Cos Sum Formula
⏱️ 0:431🎬 EYIrakrIAzw
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011. Q11b

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Answer
📚 Related Lectures
12.3.2 ADVFUN, TRIG, SUM FORMULA, given.Two.Ratios, find.Sum.Ratio
🎓 001. Given single angles, find Sin of sum
⏱️ 0:250🎬 -tbLvGb8PFE
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011. Q11c

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Answer
📚 Related Lectures
12.3.2 ADVFUN, TRIG, SUM FORMULA, given.Sin.Cos, expand.evaluate
🎓 001. Section Intro
🎓 003. Exact Value with Sine Sum Formula
🎓 002. Exact Value with Cos Sum Formula
⏱️ 0:541🎬 tL4_Bcj-GLQ
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011. Q11d

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Answer
📚 Related Lectures
12.3.2 ADVFUN, TRIG, SUM FORMULA, given.Sin.Cos, expand.evaluate
🎓 001. Section Intro
🎓 003. Exact Value with Sine Sum Formula
🎓 002. Exact Value with Cos Sum Formula
⏱️ 0:321🎬 7DDWHVqIlo8
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012. Q12

Question
Answer
📚 Related Lectures
12.3 Advanced Function, Trigonometry, Sum Formula, Identity, prove identity.easy
🎓 001. Sum formula proof for supplementary identity
🎓 002. Sum formula proof for cofunctional identity
⏱️ 0:431🎬 hNk2pmIVFrg
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013. Q13

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Answer
📚 Related Lectures
12.3 Advanced Function, Trigonometry, Sum Formula, Identity, prove identity.medium
🎓 001. Sum formula identity proof with Diff of Sq
🎓 002. Trig identity with Sum formula, Sine to Tan ratios
⏱️ 0:321🎬 hLFNGNU1uc8
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014. Q14a

Question
Answer
📚 Related Lectures
12.3 Advanced Function, Trigonometry, Sum Formula, Identity, prove identity.medium
🎓 001. Sum formula identity proof with Diff of Sq
🎓 002. Trig identity with Sum formula, Sine to Tan ratios
⏱️ 0:431🎬 MBL91pdKlPM
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014. Q14b

Question
Answer
📚 Related Lectures
12.3.3 AdvFun, Double Angle IDENTITY, prove identity.easy
🎓 005. Double angle identity with both sin2x and cos2x
🎓 004. Double angle identity with cos2x ex1
🎓 003. Double Angle Identity on Reciprocal
🎓 002. Cos double angle formula
🎓 001. Introduction to Double Angle Formulas Sine Double Angle Formula
⏱️ 0:391🎬 q2AT3k98r9Q
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015. Q15a

Question
Answer
📚 Related Lectures
12.3 Advanced Function, Trigonometry, Double Angles, given Single Angle ratio, find.Double.Angle.Ratios
🎓 001. Introduction to Double Angles
🎓 003. Find double angle for Sine ratio given single angle
🎓 002. Given single cos, find double cos
⏱️ 2:431🎬 8DYXCqiEIdg
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38

015. Q15b

Question
Answer
📚 Related Lectures
12.3 Advanced Function, Trigonometry, Double Angles, given Single Angle ratio, find.Double.Angle.Ratios
🎓 001. Introduction to Double Angles
🎓 003. Find double angle for Sine ratio given single angle
🎓 002. Given single cos, find double cos
⏱️ 0:371🎬 I-6PuuNUTRo
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39

015. Q15c

Question
Answer
📚 Related Lectures
11.3.2 RELATIVE ACUTE ANGLES, given.Ratio.Quadrant, find.other.ratios
🎓 001. Given Ratio and Quad, find other ratios
⏱️ 0:390🎬 VyF5f2_MnDs
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40

019. Q19a

Question
Answer
📚 Related Lectures
12.3.3 AdvFun, Trigonometry, Double Angle, given double angle ratio, find single angle
🎓 001. Finding Single Angle Ratio from Double Angle Ratio
⏱️ 0:370🎬 M9znf24nYi8
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019. Q19b

Question
Answer
📚 Related Lectures
12.3.3 AdvFun, Trigonometry, Double Angle, given double angle ratio, find single angle
🎓 001. Finding Single Angle Ratio from Double Angle Ratio
⏱️ 1:550🎬 R1BjsKvS8Sg
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42

019. Q19c

Question
Answer
📚 Related Lectures
12.3.3 AdvFun, Trigonometry, Double Angle, given double angle ratio, find single angle
🎓 001. Finding Single Angle Ratio from Double Angle Ratio
⏱️ 1:030🎬 zfKO6hxlYi0
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020. Q20ab

Question
Answer
📚 Related Lectures
12.3 Advanced Function, Trigonometry, Sum Formula, Identity, prove identity.medium
🎓 001. Sum formula identity proof with Diff of Sq
🎓 002. Trig identity with Sum formula, Sine to Tan ratios
⏱️ 1:551🎬 -TWY6U_UCMc
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020. Q20c

Question
Answer
📚 Related Lectures
11 Functions, Trigonometry, evaluate special angle trig ratios
🎓 002. Evaluating Square of Ratios
🎓 001. Introduction to special angle ratios and derivations
⏱️ 2:250🎬 o87zI_Qjqeg
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021. Q21a

Question
Answer
📚 Related Lectures
12.3.2 ADVFUN, TRIG, SUM FORMULA, given.Sin.Cos, expand.evaluate
🎓 001. Section Intro
🎓 003. Exact Value with Sine Sum Formula
🎓 002. Exact Value with Cos Sum Formula
⏱️ 1:361🎬 s9bmsumwp8o
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021. Q21b

Question
Answer
📚 Related Lectures
12.3.2 ADVFUN, TRIG, SUM FORMULA, given.Sin.Cos, expand.evaluate
🎓 001. Section Intro
🎓 003. Exact Value with Sine Sum Formula
🎓 002. Exact Value with Cos Sum Formula
⏱️ 1:260🎬 BXAcHMDMc5E
▶ Watch
47

022. Q22a

Question
Answer
📚 Related Lectures
12.3 Advanced Function, Trigonometry, Sum Formula, Identity, prove identity.medium
🎓 001. Sum formula identity proof with Diff of Sq
🎓 002. Trig identity with Sum formula, Sine to Tan ratios
⏱️ 0:501🎬 _5yDkk4PsIM
▶ Watch
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023. Q23a

Question
Answer
📚 Related Lectures
12.3 Advanced Function, Trigonometry, Sum Formula, Identity, prove identity.medium
🎓 001. Sum formula identity proof with Diff of Sq
🎓 002. Trig identity with Sum formula, Sine to Tan ratios
⏱️ 3:371🎬 3I0E-th4emY
▶ Watch
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023. Q23b

Question
Answer
📚 Related Lectures
12.3.3 AdvFun, Trigonometry, Sum to Product, prove identity.medium
🎓 001. Using sum to product formula to prove an identity
⏱️ 1:061🎬 Vb_N2CgHF68
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50

024. Q24a

Question
Answer
📚 Related Lectures
12.3 Advanced Function, Trigonometry, Double Angles, given Single Angle ratio, find.Double.Angle.Ratios
🎓 001. Introduction to Double Angles
🎓 003. Find double angle for Sine ratio given single angle
🎓 002. Given single cos, find double cos
⏱️ 1:431🎬 k0Tt1mSr0yI
▶ Watch
51

024. Q24b

Question
Answer
📚 Related Lectures
12.3 Advanced Function, Trigonometry, Double Angles, given Single Angle ratio, find.Double.Angle.Ratios
🎓 001. Introduction to Double Angles
🎓 003. Find double angle for Sine ratio given single angle
🎓 002. Given single cos, find double cos
⏱️ 1:310🎬 S9yVnyozBBA
▶ Watch
52

025. Q25

Question
Answer
⏱️ 1:520🎬 QS1JpY77hsA
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53

026. Q26

Question
Answer
📚 Related Lectures
12.3 Advanced Function, Trigonometry, Sum Formula, Identity, prove identity.medium
🎓 001. Sum formula identity proof with Diff of Sq
🎓 002. Trig identity with Sum formula, Sine to Tan ratios
⏱️ 2:490🎬 K6qZIniE9us
▶ Watch
54

028. Q28

🎬 ZzQ5xIYGVyc
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