Math 150: Trigonometry - Special Angles and the Trigonometry of the Unit Circle - Mathematics Assignment Help

Assignment Task:

Task:

1) Suppose that the point is a point on the unit circle lying in quadrant III. Find the values of all 6 trigonometric functions of where is the smallest positive angle whose terminal side is the ray that contains the point

2) Consider the points that lie on circles of radius 1 and 5 and that lie on the terminal side of an angle, in standard form, of 5 radians. Draw a realistic sketch of the situation and find trigonometric representations of these two points.

3) Without looking at any notes label all special angles (you will need to do this from memory without notes—in calculus, your next course, it is expected that you are able to do this without notes) including quadrantal angles, in both degrees and radians, and label the corresponding points on the unit circle.

4) Find the exact values of , and if

5) Find the exact values of , and if

6) Find the exact values of , and if

7) Find the exact values of , and if

Derive: to reach or obtain by reasoning.
8) Area bounded by chord and circumference:
a) Consider the shaded portion of the image. Derive, showing all work, a formula for the shaded portion of the image that gives the area of the shaded region as a function of the radius of the circle and as a function of the measure of the central angle theta. When you are finished, your formula should contain r, and . Hint: Establish an -coordinate system that puts the angle theta in standard position.
b) Use your formula from part a to find the exact (no approximations, no rounding) area of the shaded region in the figure below.

c) Approximate the area of the shaded region by rounding your previous answer to the nearest 100th.

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