if cos of theta= -4/5 and tan of theta > 0, find sin of theta
cos negative means quadrant II, or quadrant III.
TanTheta is >0 in first quadrant, third quadrant.
So theta is in quadrant III, which means SinTheta is negative.
if cos=4/5, sin = 3/5 but has to be negative, or sinTheta=-3/5
To find the sine of theta, we can use the Pythagorean identity:
sin^2(theta) + cos^2(theta) = 1.
Given that cos(theta) = -4/5, we can substitute this value into the equation to find sin(theta):
sin^2(theta) + (-4/5)^2 = 1.
To solve for sin(theta), we first need to find sin^2(theta). Rearranging the equation, we have:
sin^2(theta) = 1 - (-4/5)^2.
Calculating this, we get:
sin^2(theta) = 1 - 16/25
= 9/25.
Now, we can take the square root of both sides to find sin(theta):
sin(theta) = ±sqrt(9/25).
Since tan(theta) is positive, we know that sine and cosine have the same sign. Therefore, we can discard the negative solution and conclude that:
sin(theta) = sqrt(9/25)
= 3/5.
Hence, the sine of theta is 3/5.