Trigonometry I

Question 1

What is the fundamental trigonometric identity?

Answer 1

sin^2 θ + cos^2 θ = 1

Question 2

What are the cofunction identities of sine and cosine?

Answer 2

sin x = cos (90 - x)
cos x = sin (90 - x)

note: x can also be θ

Question 3

What are the cofunction identities of tangent and cotangent?

Answer 3

tan x = cot (90 - x)
cot x = tan (90 - x)

note: x can also be θ

Question 4

What are the cofunction identities of secant and cosecant?

Answer 4

sec x = csc (90 - x)
csc x = sec (90 - x)

note: x can also be θ

Question 5

What is the quotient function of tangent?

Answer 5

tan is y/x, or sin θ/cos θ

Question 6

What is the quotient function of cotangent?

Answer 6

cotan is x/y, or cos θ/sin θ

Question 7

What is the reciprocal function for sin?

Answer 7

sin θ = 1/csc θ

note: sin is O/H, csc is H/O

Question 8

What is the reciprocal function for cos?

Answer 8

cos θ = 1/sec θ

note: cos is A/H, sec is H/A

Question 9

What is the reciprocal function of tan?

Answer 9

tan θ = 1/cot θ

note: tan is O/A, c is A/O

Question 10

What is the complementary angle rule?

Answer 10

The sin (O/H) of an angle = the cos (A/H) of its complementary angle.

Question 11

What is 90 degrees in radians?

Answer 11

π/2

Question 12

What is 180 and 360 degrees in radians, respectively?

Answer 12

π and 2π

Question 13

What can the law of sines be used for?

Answer 13

to find the 3rd side; when two sides and the angle between them is known

Question 14

What is the law of sines?

Answer 14

In any △, the ratio of the sin of an angle to the opposite side length is equal for all 3 angles and sides.

Question 15

What can the law of cosines be used for?

Answer 15

to find the other two sides; if 2 angles and one side is known

Question 16

What is the law of cosines?

Answer 16

In any △, the square of a side is equal to the sum of the squares of the other two sides minus the two sides’ product and the cosine of the opposite angle.

or: a^2 = b^2 + c^2 - 2bc cos(A)

Question 17

What letters denote angle measures in the law of sines and cosines?

Answer 17

A, B, C

Question 18

What letters denote side length measures in the law of sines and cosines?

Answer 18

a, b, c