MATH SOLVE

5 months ago

Q:
# If sinθ = 3/4 and is in the first quadrant, then cosθ = _____.

Accepted Solution

A:

The trick here is to recognize that "sin omega = 3/4" provides us with the length of the opposite side of a first-quadrant triangle and the length of the hypotenuse; they are 3 and 4 respectively.

Find the length of the adjacent side (x) using the Pythagorean Theorem: 3^2 + x^2 = 4^2, or x^2 = 16 - 9 = 7. Then the length of the adj. side, x, is sqrt(7).

The cosine of omega is adj / hyp, or sqrt(7) / 4.

Find the length of the adjacent side (x) using the Pythagorean Theorem: 3^2 + x^2 = 4^2, or x^2 = 16 - 9 = 7. Then the length of the adj. side, x, is sqrt(7).

The cosine of omega is adj / hyp, or sqrt(7) / 4.