Question

If θ is a Quadrant II angle and cosθ = -2/3 , then sinθ = _____.

Answer 1

See the attached picture. If a point P(x, y) is on the terminal side of an angle theta.


`\cos(\theta) = (x)/(r)`

In this case, x = -2 and r = 3. Use the Pythagorean Theorem to find the value of y.


`x^2 + y^2 =r^2 \\ 4+y^2=9 \\ y^2 = 5 \\ y=√(5)`

Note that you pick the positive square root for y because the point is in Quadrant II.

Now,
`\sin(\theta) = (y)/(r) = (√(5))/(3)`