Question

Evaluate cosθ if sinθ = ="\frac{ \sqrt{5} }{3} " alt="\frac{ \sqrt{5} }{3} " align="absmiddle" class="latex-formula">

Answer 1

We are told that sin theta = sqrt(5) / 3.  Thus, the opp side of this angle is sqrt(5), and the hypo is 3.  Use the Pythagorean Theorem to find the adj side:

[sqrt(5)]^2 + adj^2 = 3^2, or 5 + adj^2 = 3^2.  Thus, 5 + adj^2 = 9.  Solving for adj, we get adj = plus or minus 2.

The angle theta could be in either QI or QIII, because the sine is positive.  

If the angle theta is in QI, the cosine of theta is -2/3; if in QIII, 2/3.