SOLUTION: Solve the equation cos2x + sin^2x = 4/9 to the nearest hundredth where 0 ≤ x ≤ 2π. Link to equation composition: https://gyazo.com/272cf3acc8fa67872432b81fdcbebe62

Algebra ->  Functions -> SOLUTION: Solve the equation cos2x + sin^2x = 4/9 to the nearest hundredth where 0 ≤ x ≤ 2π. Link to equation composition: https://gyazo.com/272cf3acc8fa67872432b81fdcbebe62      Log On


   

Question 1205304: Solve the equation cos2x + sin^2x = 4/9 to the nearest hundredth where 0 ≤ x ≤ 2π.
Link to equation composition: https://gyazo.com/272cf3acc8fa67872432b81fdcbebe62
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

cos%282x%29+%2B+sin%5E2%28x%29+=+4%2F9 .... where 0+%3C=+x+%3C=+2pi

cos%282x%29+%2B+sin%5E2%28x%29+=+4%2F9
use identity+cos%282x%29=cos%5E2%28x%29+-+sin%5E2%28x%29
cos%5E2%28x%29+-+sin%5E2%28x%29+%2B+sin%5E2%28x%29+=+4%2F9
cos%5E2%28x%29+=+4%2F9
cos%28x%29+=sqrt+%284%2F9%29
cos%28x%29+=2%2F3

solutions in given interval:
x=cos%5E-1%282%2F3%29
x=0.84106867
x=48.19°

x=cos%5E-1%28-2%2F3%29
x=2.3005239
x=131.8°

x=2pi-cos%5E-1%282%2F3%29
x=5.4421166
x=311.81°

x=2pi-cos%5E-1%28-2%2F3%29
x=3.9826613241
x=228.19°