Question

If cos(t)=24/25 and t is in the fourth quadrant find sin(t).

Answer 1

To find sin(t) with cos(t)=24/25 and t in the fourth quadrant, use the Pythagorean identity to solve for sin(t) which yields -7/25 because sine is negative in the fourth quadrant.

Step-by-step explanation:

If cos(t)=24/25 and t is in the fourth quadrant, the value of sin(t) needs to be determined. Knowing that in the fourth quadrant, cosine is positive, and sine is negative, we can use the Pythagorean identity sin2(t) + cos2(t) = 1 to find the value of sin(t).

First, plug the given cosine value into the identity:

sin2(t) + (24/25)2 = 1

Then, simplify and solve for sin2(t):

sin2(t) + (576/625) = 1

sin2(t) = 1 - (576/625)

sin2(t) = (625 - 576) / 625

sin2(t) = 49 / 625

Since sin(t) is negative in the fourth quadrant:

sin(t) = -sqrt(49 / 625)

sin(t) = -7/25