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. Go back and review all of this Trigonometric Functions chapter if you are lost.
Examples Involving the Trig Functions
Find the value of
1. cos(π/6)
2. sec 4.5
3. sec 4.5°
- Answers
-
1. cos(π/6) (= cos30°) = 0.8660254
2. sec 4.5 = -4.7439275
3. sec 4.5° = 1.0030922
Notice the difference between these last two. Without the degree sign, 4.5 means "4.5 radians". It is important to set your calculator properly before starting these problems.
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
-
a)
b) 
2. Express the following angles in degrees:
a) 
b) 
- Answer
-
a)
b) 
3. Express in radian measure (use decimals): 168.7°
- Answer
-
4. Express in terms of degrees: 1.703
- Answer
-
5. Find 
- Answer
-
6. Find sin 2.34
- Answer
-
sin 2.34 = 0.7185
7. Find θ if cos θ = -0.9135 (0 ≤ θ < 2π)
- Answer
-
cos θ = -0.9135 (0 ≤ θ < 2π )
α = 0.41899 radians
Since cos θ is negative, it means θ is in the second and third quadrants.
θ = π - 0.41899 = 2.723 or
θ = π + 0.41899 = 3.561
8. Find θ if csc θ = 3.940 (0 ≤ θ < 2π)
- Answer
-
If csc θ = 3.940 , then
α = 0.2566.
Now θ is in the first and second quadrants because csc θ is positive.
So
θ = 0.2566 or
θ = π - 0.2566 = 2.8850
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