Use the figure to answer the following questions Use the fig

Use the figure to answer the following questions.

Use the figure below to answer the following questions. Approximate the measure of the indicated angle, theta, measured in radius. Radians Using the figure above, and without using a calculator, approximate the value of 5 sin (theta) Using your answer from part(b), approximate the value of sin (theta). Using the figure above, and without using a calculator, approximate the value of 5 cos(theta). Using your answer from part(d), approximate the value of cos(theta).

Solution

if we draw a perpendicular from the point where line making angle theta

cuts the circle to the -ve x axis , it falls on -ve x axis at point between -1.5 and -1

so,right angled triangle with acute angle 180 - theta has base of x = 1.25

So, cos(180 - theta) = - 1.25/5

5cos(theta) = -1.25

cos(theta) = - 0.25

theta = 104.47 deg = 1.82 rad

sin(theta) = sqrt( 1 - cos^2(theta) ) = sqrt( 1 - 0.25^2) = 0.968

5sin(theta) = 4.84