Show Work Assignment: Solving Basic Trigonometric Equations

What you do:

Solve the equation sin = - 0.78 algebraically.

This means that you are not using your calculator to find the points of intersection, but you are solving on paper. You must include all calculations for credit. Your answer must be in radians and capture all solutions in the reals.

In your canvas modules, there are many videos on solving trigonometric equations, and two specifically on solving a basic sine equation. You will find the two videos in canvas modules, "Videos (Part 2): Solving Basic Trigonometric Equations." The titles of the two videos on solving a basic sine equation are:

1) Solving a Basic Sine Equation (sinx = 0.57) 17:49

2) Solving a Basic Sine Equation (sinx = - 0.67) 8:51

As you can see, the first video is much longer than the second video, because I include what you are finding graphically, and I go into more depth about details of the solution process. I recommend watching both videos before submitting your work so that you understand what work you need to provide. Some tips to make sure you include all the work I am looking for:

a) When solving for theta, include a rough sketch of a unit circle (by rough sketch you need only show the specific angle you're finding, not all the angles of the unit circle), and label what you're finding on the reference triangle (that is, are you finding x, y, or y/x?).

b) When solving for the other solution that the calculator does not provide, also show a rough sketch of a unit circle, the location of the other angle, and what it is you're finding on the reference triangle.

c) Your answer must capture all solutions in the reals, so you will be using an integer in your solution; please define the letter you use as an integer. Your specific angles must go out 4 decimal places.