Use the given information to determine the exact trigonometric value. sin(theta)= -1/5, pi< (theta) < 3pi/2, cos(theta)

Question

i dont know how to do this

Answer 1

Hi Kelsey,

Since pi< (theta) < 3pi/2, we are in the third quadrant. Both sin and cos functions are negative in this quadrant. 

sin(theta) = -1/5. This means that we have a right triangle with opposite side length 1 unit and hypotenuse length 5 units because sin(theta)=opp/hyp.

To find cos(theta) we need to find the adjacent side because cos(theta=adj/hyp

Use the pythagorean theorem.

5^2 = 1^2 + x^2  where x is the adjacent side length

x = sqrt(24)

= 2√6 units

Then, cos(theta) = -2√6 / 5.