Question

Given sine (t) = startfraction 7 over 25 endfraction for startfraction pi over 2 endfraction less-than t less-than pi, what is cos(t)? startfraction 24 over 25 endfraction startfraction 7 over 24 endfraction negative startfraction 7 over 24 endfraction negative startfraction 24 over 25 endfraction

Answer 1

Answer:

  (d)  -24/25

Step-by-step explanation:

The given angle is in the second quadrant, where the sine is positive and the cosine is negative.

Cosine

The relation between sine and cosine tells you ...

  cos(t)² = 1 -sin(t)²

  cos(t)² = 1 -(7/25)² = (625 -49)/625 = 576/625

Taking the negative square root, we have ...

  cos(t) = -√(576/625)

  cos(t) = -24/25