Question

If sin theta equal 2/3 and theta is in Quadrant 1, then what value of (tan theta)(cos theta)? Help Please!

A-2/3
B-3 square root 5/5
C-2 square root 5/3
D-square root 5/3

Answer 1

Option A. 2/3

Explanation:

we know that

If angle theta is in Quadrant 1

then

The value of cos(theta) is positive and the value of tan(theta) is positive

Remember that

tan(theta)=sin(theta)/cos(theta)

In this problem we have

tan(theta)*cos(theta)=[sin(theta)/cos(theta)]*cos(theta)=sin(theta)

therefore

tan(theta)*cos(theta)=sin(theta)=2/3