Question

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

Answer 1

Answer:

Step-by-step explanation:

sin(θ) = 2/7

sin²(θ) +cos²(θ) =1

$(\frac{2}{7})^{2} +cos^2(theta)=1 \\\\cos^2(theta)=1-(\frac{4}{49} )=\frac{49}{49}-\frac{4}{49} =\frac{45}{49} \\ \\cos(theta)=+/-\sqrt{\frac{45}{49} } =+/-\frac{3\sqrt{5} }{7}$

$Answer \\ is \frac{3\sqrt{5} }{7}$

Answer is positive because tangent is positive, sin is also positive, and tan=sin/cos.