1. Ch. 8 – Trig Equations
and Applications
8.1 Simple Trig Equations
Objectives:
1. Solve and apply simple trig
equations

2. To Solve:
 Isolate the trig function on one side.
 Use inverse trig function on calc. to
find reference angle.
 Find other angles within given
restrictions.

3. Example:
 Find the values of x between 0 and
2π for which sin x = 0.6.

4. Example:
 To the nearest tenth of a degree,
solve 3 cos θ + 9 = 7 for 0 ≤ θ < 360°

5. You Try!
 To the nearest hundredth of a
radian, solve 3 sin x + 2 = 4
for 0 ≤ x < 2π

6. Inclination and Slope
 A line’s inclination is the angle α,
where 0° ≤ α < 180°, that is measured
from the + x-axis to the line.
 How can we find the slope?

7. Theorem
 For any line with slope m and
inclination α:
 If α = 90°, the line is vertical and its
slope is undefined.

8. Example:
 The inclination of a line is 140°, find
its slope to the nearest hundredth.

9. You Try!
 Find the slope and equation of the line
with inclination 45° and y-intercept
(0, 4).

10. Example
 To the nearest degree, find the
inclination of the line 2x + 5y = 15.

11. You Try!
 To the nearest degree find the
inclination of the line joining the
points (-3, -5) and (3, -3)

12. More Solving
 Solve for 0 ≤ x < 2π without a
calculator:

13. You Try!
 Solve for 0 ≤ x < 2π without a
calculator: