William W. answered • 01/31/20
Math and science made easy - learn from a retired engineer
Draw a coordinate plane with a circle about the origin. The directions say to work in quadrant 1 (that is where the angle (x) is greater than 0 and less than π/2). Then draw a point on the circle in Q1 and make a right triangle that has one vertex at the origin, one at the point on the circle you drew, and one on the x-axis. Think of the reference angle as "x". Since tan(x) = opposite/adjacent = 3/4, call the opposite side 3 and the adjacent side 4. Like this:
Use the Pythagorean Theorem to solve for the hypotenuse:
hyp = √(32 + 42) = 5
Now, we need to subtract 3π/2 from "x" meaning we go clockwise 3π/2 radians (270°). Rotating the hypotenuse is the easiest thing to do and then you can re-create the triangle. First, rotating the hypotenuse 180° (π radians) will essentially just be an extension of the existing hypotenuse onto the opposite side of the circle. Then go another 90° (π/2 radians) which will put you in Q2. It will result in the same triangle, just lying down. Like this:
The cos(x-3π/2) = adj/hyp = -3/5. Notice that the x-value is negative (-3) because you are in Q2.
Repeat the process for the second problem.
