Chapter Contents

• Trigonometric Functions
• 1. Angles
• 2. Sine, Cosine, Tangent & Reciprocals
• 3. Values of Trigonometric Functions
• 4. The Right Triangle and Applications
• Trigonometry Revision Summary
• 5. Signs of the Trigonometric Functions
• 6. Trigonometric Functions of Any Angle
• 7. Radians
• 8. Applications of Radian Measure
• Pulleys
• 9. Radians and the Trigonometric Ratios
• Trigonometric Functions Problem Solver

• Comments, Questions?

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9. Radians and the Trigonometric Ratios

In this section we see examples of how to use radians instead of degrees when finding the values of sin, cos, tan, csc, sec and cot of angles.

We are using all that we have learned in this chapter. If you are lost:

• Go back and review this Trigonometric Functions chapter.
• See this simple introduction to radians with an interactive graph.

Examples Involving the Trig Functions

Find the value of

1. `cos(pi/6)`

2. `sec\ 4.5`

3. `sec\ 4.5^"o"`

Answer

Now it's your turn to try the following exercises.

Exercises

1. Express in radian measure in terms of π:

a) `12°` b) `225°`

Answer

2. Express the following angles in degrees:

a) `(7pi)/15` b) `(4pi)/3`

Answer

3. Express in radian measure (use decimals): `168.7^"o"`

Answer

4. Express in terms of degrees: `1.703\ "radians"`

Answer

5. Find `tan((4pi)/3)`

Answer

6. Find `sin\ 2.34`

Answer

7. Find ` θ` if `cos\ θ = -0.9135 (0 ≤ θ < 2π)`

Answer

8. Find `θ` if `csc\ θ = 3.940\ (0 ≤ θ < 2π)`

Answer