Published on March 16, 2014
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 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?
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:
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8.1 Simple Trig Equations. There are often multiple (infinite) solutions to trigonometric equations. For example take the equation sin(x)=.5. Find the.
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