8 1 simple trig equations

Ch. 8 – Trig Equations and Applications

8.1 Simple Trig Equations

Objectives:

1. Solve and apply simple trig equations

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.

Example:

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

Example:

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

You Try!

To the nearest hundredth of a radian, solve 3 sin x + 2 = 4 for 0 ≤ x < 2π

Inclination and SlopeA 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?

Theorem

For any line with slope m and inclination α:

If α = 90°, the line is vertical and its slope is undefined.

Example:

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

You Try!

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

Example

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

You Try!

To the nearest degree find the inclination of the line joining the points (-3, -5) and (3, -3)

More Solving

Solve for 0 ≤ x < 2π without a calculator:

You Try!

Solve for 0 ≤ x < 2π without a calculator: