10/27/22 - Tangent Function and Inverse Trig Functions

Question 1

How is tan(θ) defined in relation to sin and cos?

Answer 1

tan(θ) = (sin θ)/(cos θ)

Question 2

How is tan(θ) defined in relation to the unit circle?

Answer 2

tan(θ) = the slope of a line through the origin and reference point.

Question 3

What is arcsin(x)?

Answer 3

An angle θ in the interval [-90 degrees, 90 degrees] such that x = sin(θ).
x is in [-1, 1]

Question 4

What is arccos(x)?

Answer 4

An angle θ in the interval [0, 180 degrees] such that x = cos(θ)
x is in [-1, 1]

Question 5

What is arctan(x)?

Answer 5

An angle θ on the interval (90 degrees, -90 degrees) such that x = tan(θ).
x is in (-∞, ∞)

Question 6

What is arcsin(1/2)

Answer 6

1/2 = sin(θ), θ = 30 degrees
arcsin(1/2) = 30 degrees

Question 7

What is arcsin(-1/2)?

Answer 7

-30 degrees

Question 8

What is arctan(1)?

Answer 8

tan(θ) = 1
(sin θ)/(cos θ) = 1
sin(θ) = cos(θ), so θ = 45 degrees
arctan(1) = 45 degrees