316,976 views
28 votes
28 votes
If cos2β = 3/4 and ß terminates in quadrant III, find cosβ :

User Minh Bui
by
2.4k points

1 Answer

17 votes
17 votes

Answer:

cosβ = -1/2

Explanation:

Since cos2β = 3/4 and β is in quadrant III, the value of cosβ must be negative. We can find the exact value of cosβ by using the identity cos2β = 2cos^2β - 1. Substituting 3/4 for cos2β and solving for cosβ, we get:

3/4 = 2cos^2β - 1

cos^2β = 1/4

cosβ = 1/2 or -1/2

Since cosβ is negative in quadrant III, the value of cosβ is -1/2. Thus, the answer is cosβ = -1/2.

Tell me if this helped :)

User Zionpi
by
2.9k points