Question

If sin θ = 2/7 and tan θ > 0, what is the value of cos θ?

Answer 1

First, use sin θ = 2/7 to make a right-triangle.

Answer 2

I don'tunderstandhow

Answer 3

You know sin θ = opp/hyp right?? Try making a triangle..

Look at these:

sin θ = opp/hyp
sin θ = 2/7

Now tell me... What is opposite and what is hypotenuse?

Answer 4

Sin theta is positive, so theta is in either the 1st or 2nd quadrant.

Tan theta is positive (given in qn), so theta is in either the 1st or the 3rd quadrant.

Taking the intersection of the possibilities of the quadrants theta might lie in,

Theta lies in the 1st quadrant.

Answer 5

By Pythagoras' Theorem, the unknown side is
\[\sqrt{49-4}=\sqrt{45}\]
\[\cos \theta = \frac{ \sqrt{45} }{ 7 }\]