Question

Use the fundamental identities to find the value of trigonometric function

find sin theta if cos theta =2/3 and theta is in quad iv

Answer 1

Answer: Since cos(theta) = 2/3 and theta is in quadrant IV, we know that sin(theta) is negative. We can use the Pythagorean identity to find the value of sin(theta):

sin^2(theta) + cos^2(theta) = 1

Substituting cos(theta) = 2/3, we get:

sin^2(theta) + (2/3)^2 = 1

Simplifying, we get:

sin^2(theta) = 1 - (2/3)^2 = 1 - 4/9 = 5/9

Since sin(theta) is negative in quadrant IV, we have:

sin(theta) = -sqrt(5/9) = -sqrt(5)/3

Therefore, sin(theta) = -sqrt(5)/3.

Explanation: