Question

find the period of sin^2x+2cos^2x​

Answer 1

Pi
.............................

Answer 2

Answer: pi

Step-by-step explanation:

sin^2(x) + cos^2(x) = 1

so: sin^2(x) + 2 cos^2(x) = cos^2(x) + 1

cos(2x) = 2 cos^2(x) - 1

so: (cos(2x) + 1)/2 = cos^2(x)

and so: (cos(2x) - 1)/2 = cos^2(x) + 1

The initial expression is equal to (cos(2x) - 1)/2

The period of cos(x) is 2 pi, in our equation we have cos(2x), which is a horizontal stretch of the graph of cos(x) by 1/2. This is the same as saying the period is divided by 2, so the answer is pi.

The actual formula for finding the period of a cos(x) graph is:

p = 2pi/b , where b comes from: a(cos(b(x - c))) + d