PRE CALCULUS Trigonometry

Question 1

What is sin(30°)?

Accepted Answer

1/2

Answer

sin(30°) = 1/2 is one of the fundamental trigonometric values that should be memorized, derived from the 30-60-90 special right triangle.

Question 2

What is the unit circle?

Accepted Answer

A circle with radius 1 centered at the origin, used to define trigonometric functions for all angles

Answer

The unit circle has radius 1 and center at (0,0). Any point on it has coordinates (cos θ, sin θ), defining trig functions for all angles.

Question 3

What is the period of the standard sine function y = sin(x)?

Accepted Answer

2π

Answer

The sine function completes one full cycle every 2π radians (360°), returning to its starting value after this interval.

Question 4

What is the Pythagorean identity?

Accepted Answer

sin²θ + cos²θ = 1

Answer

sin²θ + cos²θ = 1 is the fundamental Pythagorean identity, derived from the Pythagorean theorem applied to the unit circle.

Question 5

What is the tangent of an angle in terms of sine and cosine?

Accepted Answer

tan θ = sin θ / cos θ

Answer

Tangent is defined as the ratio of sine to cosine: tan θ = sin θ / cos θ. This is undefined when cos θ = 0.

PRE CALCULUS Practice Test