Trigonometric Functions: The Unit Circle Section 4.2 Objectives Find a point on the unit circle given one coordinate and the quadrant in which the point lies. Determine the coordinates of a point on the unit circle given a point on the unit circle. State the sign of the sine or cosine valu...
(b) Visualize the Unit Circle: Understand and visualize the unit circle, as it can help in remembering the sine and cosine values for common angles. (c) Relate to Special Triangles: Memorize the properties of 30°-60°-90° and 45°-45°-90° triangles. These triangles reflect the sine...
The Unit Circle We are going to fill in values on our unit circle. “Special Angles” on the unit circle 30, 60, 90 and 45, 45, 90 “Special Angles” on unit circle give “special points” on the unit circle. Evaluating Trig Functions Given a point (x,y) on the unit circle, the...
If we look at the unit circle below, (0,1) (x,y) 1 (-1,0) (1,0) (0,-1) and let (x,y) be any point on the circle, then and cosx, and siny. To see this simply examine the triangle above and use the previous definitions of these functions. Thus to find the sines and ...
Example 1: Solve: ∫ sin 2x cos 3x dx. Solution: Given: ∫ sin 2x cos 3x dx. Now, by using thetrigonometric identitysin x cos y = (½)[sin(x+y) + sin (x-y)] Therefore, ∫ sin 2x cos 3x dx = (½)[∫ sin 5x dx –∫sin x dx] ...