Find the exact value of sin(θ) for an angle θ with sec(θ) = 5/2 and with its terminal side in Quadrant IV.
+23246 Draw a picture!
It's in Quadrant IV, so the x-value (cos) will be positive and the y-value (sin) will be negative.
sec(theta) = 5/2 ---> 1/cos(theta) = 5/2 ---> cos(theta) = 2/5
In your reference triangle, the x-value = 2 and the hypotenuse = 5
Using the Pytagorean Theorem, the y-value = - sqrt(21)
sin = y / r ---> sin(theta) = - sqrt(21) / 5
I think that the best way to approach these problems is to draw the picture ...
