What is the formula and solution of this problem an angle of 50 degrees in standard position has its terminal side in the first quadrant. find the coordinates of point P on the unit circle.?

Answer 1

This is somewhat difficult to explain without images, but here goes:

You can use the information given in the problem to draw a right triangle on your coordinate axes. The hypotenuse of this right triangle should extend from the origin to point P and make a 50 degree angle with the x-axis. We'll call this hypotenuse r, which in this case is 1 (because we're dealing with the unit circle). If you extend a line down from point P perpendicular to the x-axis, the segment formed, which we will call y, will be the side of the right triangle opposite the 50 degree angle. The remaining side, x, lies along the x-axis between the origin and the point where side y intercepts the x axis.

Recognize that side x and side y represent, respectively, the x and y coordinates of P. These values can be found using trigonometric relationships.

Recall that sin(a) = opposite/hypotenuse. In this case, a = 50, the opposite side is y, and the hypotenuse is r=1, so we can rewrite this equation as

sin(50) = y/r = y

Which means that y is simply sin(50).

Similarly, cos(a) = adjacent/hypotenuse, so cos(50) = x/r = x. x = cos(50).

P is therefore located at (cos[50], sin[50])