Trig Laws and Idenities (AI)

Question 1

What is the Pythagorean Identity?

Answer 1

sin^2(theta) + cos^2(theta) = 1

Question 2

What is the Reciprocal Identity for sine?

Answer 2

csc(theta) = 1/sin(theta)

Question 3

What is the Reciprocal Identity for cosine?

Answer 3

sec(theta) = 1/cos(theta)

Question 4

What is the Reciprocal Identity for tangent?

Answer 4

cot(theta) = 1/tan(theta)

Question 5

What is the Quotient Identity for tangent?

Answer 5

tan(theta) = sin(theta)/cos(theta)

Question 6

What is the Even-Odd Identity for sine?

Answer 6

sin(-theta) = -sin(theta)

Question 7

What is the Even-Odd Identity for cosine?

Answer 7

cos(-theta) = cos(theta)

Question 8

What is the Cofunction Identity for sine?

Answer 8

sin(90 - theta) = cos(theta)

Question 9

What is the Cofunction Identity for cosine?

Answer 9

cos(90 - theta) = sin(theta)

Question 10

What is the Half-Angle Identity for sine?

Answer 10

sin(2theta) = 2sin(theta)cos(theta)

Question 11

What is the Half-Angle Identity for cosine?

Answer 11

cos(2theta) = cos^2(theta) - sin^2(theta)

Question 12

What is the Double-Angle Identity for sine?

Answer 12

sin(2theta) = 2sin(theta)cos(theta)

Question 13

What is the Double-Angle Identity for cosine?

Answer 13

cos(2theta) = cos^2(theta) - sin^2(theta)

Question 14

What is the Addition Identity for sine?

Answer 14

sin(alpha + beta) = sin(alpha)cos(beta) + cos(alpha)sin(beta)

Question 15

What is the Addition Identity for cosine?

Answer 15

cos(alpha + beta) = cos(alpha)cos(beta) - sin(alpha)sin(beta)

Question 16

What is the Subtraction Identity for sine?

Answer 16

sin(alpha - beta) = sin(alpha)cos(beta) - cos(alpha)sin(beta)

Question 17

What is the Subtraction Identity for cosine?

Answer 17

cos(alpha - beta) = cos(alpha)cos(beta) + sin(alpha)sin(beta)

Question 18

What is the Cofunction Identity for tangent?

Answer 18

tan(90 - theta) = cot(theta)

Question 19

What is the Tangent Addition Identity?

Answer 19

tan(alpha + beta) = (tan(alpha) + tan(beta))/(1 - tan(alpha)tan(beta))

Question 20

What is the Tangent Subtraction Identity?

Answer 20

tan(alpha - beta) = (tan(alpha) - tan(beta))/(1 + tan(alpha)tan(beta))

Question 21

What is the Tangent Double-Angle Identity?

Answer 21

tan(2theta) = (2tan(theta))/(1 - tan^2(theta))

Question 22

What is the Cotangent Double-Angle Identity?

Answer 22

cot(2theta) = (cot^2(theta) - 1)/(2cot(theta))

Question 23

What is the Law of Sines?

Answer 23

a/sin(alpha) = b/sin(beta) = c/sin(gamma)

Question 24

What is the Law of Cosines?

Answer 24

c^2 = a^2 + b^2 - 2abcos(gamma)