Trig Identities Yr 2

Question 1

What is the proof for the formula

Answer 1

Question 2

What is the equation for the following ?

Answer 2

Question 3

What is the equation for the following ?

Answer 3

Question 4

How can you use the identity sin(A+ B) = sin (A) cos (B) + cos(A) sin(B) to prove the identity for sin (A-B)?

Answer 4

Question 5

What is the double angle formula for sin?

Answer 5

sin(2θ) = 2sin(θ)cos(θ)

Question 6

What is the double angle formula for cos?

Answer 6

cos(2θ) = cos²(θ) - sin²(θ)

Question 7

What is the double angle formula for tan?

Answer 7

tan(2θ) = (2tan(θ))/(1 - tan²(θ))

Question 8

Fill in the blank: cos(2θ) = ______ - ______.

Answer 8

cos²(θ), sin²(θ)

Question 9

What is the double angle formula for cos in terms of sin?

Answer 9

cos(2θ) = 1 - 2sin²(θ)

Question 10

What is the double angle formula for tan in terms of sin and cos?

Answer 10

tan(2θ) = (2tan(θ))/(1 - tan²(θ)) = (2sin(θ)cos(θ))/(cos²(θ) - sin²(θ))

Question 11

What is the compound angle formula for sin(A + B)?

Answer 11

sin(A + B) = sin(A)cos(B) + cos(A)sin(B)

Question 12

What is the compound angle formula for cos(A + B)?

Answer 12

cos(A + B) = cos(A)cos(B) - sin(A)sin(B)

Question 13

What is the compound angle formula for tan(A + B)?

Answer 13

tan(A + B) = (tan(A) + tan(B)) / (1 - tan(A)tan(B))

Question 14

What is the compound angle formula for Sin (A- B)?

Answer 14

sin(A) cos (B) - cos (A) sin(B)

Question 15

What is the compound angle formula for Cos (A-B)?

Answer 15

Cos (A) Cos(B) + sin (A) sin(B)

Question 16

What is the compound angle formula for tan (A -B)?

Answer 16

( tan(A)- tan(B) )/ 1+tan(A)tan (B)

Question 17

Prove the result for cos (A +B) using sin (A+B)

Question 18

Use the identity sin (A+B) to get the formula for cos (A+B)

Answer 18

Question 19

Proving tan(A+B)

Answer 19

Question 20

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Question 21

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Question 22

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Question 23

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Question 24

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Question 25

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Question 26

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Question 27

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Question 28

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Question 29

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Question 30

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Question 31

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Question 32

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Question 33

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Question 34

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Question 35

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Question 36

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Question 37

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Question 38

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Question 39

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Question 40

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Question 41

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Question 42

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Question 43

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Question 44

What can this be represented as ?

Answer 44

Question 45

What are the equations for alpha and r?

Answer 45

Question 46

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Question 47

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Question 48

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Question 49

Answer 49

Bear in mind, the only ways that you can do when the sign between cos and sign is +. Is R sin (x+a) or R cos (x-a)

Question 50

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Question 51

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Question 52

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