Trigonometric Functions on the Unit Circle: Videos & Practice Problems

Is the point (−1/2, √3/2) on the unit circle?

Which equation represents the unit circle centered at the origin?

A company uses a simplified model where customer preference vectors lie on the unit circle. Whether the vector (0.8, 0.6) lies on the unit circle?

Convert 150° to radians.

Which point on the unit circle corresponds to the angle π/2 radians and what are its cosine and sine values?

Given a point on the unit circle at coordinates (−√2/2, √2/2), identify cosθ, sinθ and tanθ for the corresponding angle θ.

A point on the unit circle is at (0, −1). Determine cosine, sine and tangent value.

What is cos 60°, sin 30°, and tan 60°? Provide the exact simplified values.

Find exact value of tan(π/6) and provide the rationalized form if necessary.

Find the reference angle for 210° and then determine sin 210° using that reference angle and quadrant sign rules.

What is the reference angle for 315° and which standard first-quadrant angle family does it correspond to (30°, 45°, or 60°)?

According to the ASTC mnemonic, which trig functions are positive in Quadrant II?

Compute cos(150°) using the reference angle and ASTC sign rules.

Find a coterminal angle between 0 and 2π for θ = −13π/4, then evaluate sin(θ).

Which angle is coterminal with 765° and what is cos(765°)?

Determine sec(π) and csc(π/2).

Compute cot(π/3) and sec(π/2).

A startup models seasonal demand by the angle θ measured from the positive x-axis. The demand vector corresponds to a point with coordinates (−1/2, −√3/2). Identify θ in degrees between 0° and 360°.

Which of the following lists the four standard quadrantal angles in radians starting at 0 going counterclockwise?

Find sin(5π/3) by first finding its reference angle and applying quadrant sign rules.

Using the one-two-three mnemonic or left-hand rule, what are (cos45°, sin45°)?

Given an angle θ in QII with reference angle 45°, what are the coordinates on the unit circle and the values of cosθ and sinθ?

Convert 7π/4 to degrees and name the corresponding coordinate on the unit circle.

Company B models cyclic cost oscillations with angle θ = 11π/6. Determine csc θ.

Determine tan(−17π/6) by finding a coterminal angle in [0, 2π) and simplifying.

If cosθ = 2/3 for some angle θ (not on the unit circle), is secθ defined as 3/2?

A chart needs the coordinates for 120°, 225°, and 330°. Provide the ordered pairs on the unit.

Which of the following statements about tangent is true on the unit circle?

Using the left-hand rule or one-two-three rule, compute sec45° and csc60°. Provide exact values.

A financial model uses θ = 1000° in a periodic forecast. Determine sin1000° by reducing coterminally.