KKhaemenes PrecalculusTeacher Answer Key
Student Lesson

Teacher Key · Unit 04 · Lesson 06

Tangent and Reciprocal Functions on the Circle

Use this key to verify method, notation, domain, units, and interpretation. Accept equivalent exact forms when mathematically valid.

Khaemenes Academy · Teacher Key

Tangent and Reciprocal Functions on the Circle

U04 · L06
1

Convert 150° to radians.

Unitcircle visualMeasure rotation in radians and use the unit circle to connect angle, coordinate, arc length, angular velocity, and exact trigonometric values.Pθ
Answer: 5π/6
Reasoning: Multiply by π/180.
2

Convert 7π/4 to degrees.

Unitcircle visualMeasure rotation in radians and use the unit circle to connect angle, coordinate, arc length, angular velocity, and exact trigonometric values.Pθ
Answer: 315°
Reasoning: Multiply by 180/π.
3

Find an angle coterminal with −π/3 in [0,2π).

Unitcircle visualMeasure rotation in radians and use the unit circle to connect angle, coordinate, arc length, angular velocity, and exact trigonometric values.Pθ
Answer: 5π/3
Reasoning: Add 2π.
4

Find sin(5π/6).

Unitcircle visualMeasure rotation in radians and use the unit circle to connect angle, coordinate, arc length, angular velocity, and exact trigonometric values.Pθ
Answer: 1/2
Reasoning: Reference angle π/6 in Quadrant II.
5

Find cos(7π/4).

Unitcircle visualMeasure rotation in radians and use the unit circle to connect angle, coordinate, arc length, angular velocity, and exact trigonometric values.Pθ
Answer: √2/2
Reasoning: Reference angle π/4 in Quadrant IV; cosine is positive.
6

A wheel of radius 4 turns through 3π/2 radians. Find arc length.

Unitcircle visualMeasure rotation in radians and use the unit circle to connect angle, coordinate, arc length, angular velocity, and exact trigonometric values.Pθ
Answer: 6π
Reasoning: s=rθ=4(3π/2).
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