Question

If tan(theta)= 3/4 and 180 degree < theta < 270 degrees, what is sin(theta)?

Answer 1

sin(theta) = -3/5.

Explanation:

We know that tan(theta) = 3/4, which means that the ratio of the opposite side to the adjacent side of a right triangle with angle theta is 3/4. We can use the Pythagorean theorem to find the hypotenuse of the triangle:

hypotenuse^2 = opposite^2 + adjacent^2

hypotenuse^2 = (3^2) + (4^2)

hypotenuse^2 = 9 + 16

hypotenuse^2 = 25

hypotenuse = 5

Since 180 degrees < theta < 270 degrees, we know that theta is in the third quadrant, where the sine function is negative. Therefore, sin(theta) = -opposite/hypotenuse = -3/5.

So, sin(theta) = -3/5.