find sin(theta), cos(alpha), theta, alpha from picture w/ pt

Trigonometric ratios and functions, the unit circle, inverse trig functions, identities, trig graphs, etc.
Posts: 136
Joined: Sun Feb 22, 2009 11:12 pm

find sin(theta), cos(alpha), theta, alpha from picture w/ pt

I've got a picture of a unit circle with an angle theta and an angle alpha but the angles are not given. There are 2 points on the circle. Theta goes through the point (-0.985, -0.174) and alpha goes through the point (0.940, -0.342) I need to find the sine of theta and the cosine of alpha. I also need to find theta and alpha themselves.

I am confused on this one.

stapel_eliz
Posts: 1628
Joined: Mon Dec 08, 2008 4:22 pm
Contact:
Let's look at the angle theta. The terminal side passes through the point (-0.985, -0.174), which is in the third quadrant. Draw a vertical line up to the x-axis. This forms a right triangle.

Since you're on the unit circle, you know that the radius, and thus the hypotenuse of the triangle you just made, has a value of 1. What is the lenght of the side that lies on the x-axis? What is the length of the other leg? (Get this information from the point.)

You know that "sine" is "opposite over hypotenuse" and "cosine" is "adjacent over hypotenuse". So what ratio represents the sine of theta? (Read this off your picture.)

Plug that into your calculator, using the inverse-sine button (it probably looks something like "SIN-1") to find the measure of theta. Keep in mind that the inverse sine function, and thus your calculator's response, work only on the fourth and first quadrants. You'll need to adjust the value, using what you know about the sine curve, to fit.