Trig Identies

Question 1

What is cosecant?

Answer 1

csc(θ) = 1/sin(θ)

Question 2

What is secant?

Answer 2

sec(θ) = 1/cos(θ)

Question 3

What is cotangent?

Answer 3

cot(θ) = 1/tan(θ) = cos(θ)/sin(θ)

Question 4

Solve the following opposite angle trig identity:

sin(−θ)

Answer 4

sin(−θ) = −sin(θ)

Question 5

Solve the following opposite angle trig identity:

cos(−θ)

Answer 5

cos(−θ) = cos(θ)

Question 6

Solve the following opposite angle trig identity:

tan(−θ)

Answer 6

tan(−θ) = −tan(θ)

Question 7

Solve the following Angle-Sum and -Difference trig identity:

sin(α + β)

Answer 7

sin(α + β) = sin(α) cos(β) + cos(α) sin(β)

Question 8

Solve the following Angle-Sum and -Difference trig identity:

sin(α – β)

Answer 8

sin(α – β) = sin(α) cos(β) – cos(α) sin(β)

Question 9

Solve the following Angle-Sum and -Difference trig identity:

cos(α + β)

Answer 9

cos(α + β) = cos(α) cos(β) – sin(α) sin(β)

Question 10

Solve the following Angle-Sum and -Difference trig identity:

cos(α - β)

Answer 10

cos(α – β) = cos(α) cos(β) + sin(α) sin(β)

Question 11

Solve the following double angle trig identify:

sin(2θ)

Answer 11

sin(2θ)= 2sinθcosθ