sin theta = +(√23)/5
Step-by-step explanation:
Did you know that the cosine is an even function, so that cos (-theta) = cos (+theta)?
Thus we have:
cos(θ)= −√2/5 , sinθ>0
If the cosine of theta is negative, that means that the terminal side of theta is in either Quadrant II or III. Since the sine of theta is positive, we can deduce that theta is in Quadrant II.
Given cos(θ)= −√2/5, we square both sides, obtaining (cos theta)^2 = 2/25. Using the formula (sin theta)^2 + (cos theta)^2 = 1, we arrive at:
(sin theta)^2 = 1 - 2/25, or 23/25.
Then sin theta = +(√23)/5.