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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: