sin2 theta = cos theta, 90 degrees less than or equal to thetha greater than 180 degrees
To solve the equation sin^2(theta) = cos(theta) where theta is between 90 degrees and 180 degrees, we can use the trigonometric identity sin^2(theta) + cos^2(theta) = 1.
Here's how you can solve it step by step:
Step 1: Rewrite the equation using the identity sin^2(theta) + cos^2(theta) = 1:
sin^2(theta) = 1 - cos^2(theta)
Step 2: Substitute sin^2(theta) in the original equation with 1 - cos^2(theta):
1 - cos^2(theta) = cos(theta)
Step 3: Rearrange the equation to get all terms on one side:
cos^2(theta) + cos(theta) - 1 = 0
Step 4: Solve the quadratic equation. You can factorize it or use the quadratic formula:
(cos(theta) + 1)(cos(theta) - 1) = 0
This gives two possible equations:
cos(theta) + 1 = 0 or cos(theta) - 1 = 0
Solving them individually:
For cos(theta) + 1 = 0:
cos(theta) = -1
This value of cosine corresponds to the angle 180 degrees.
For cos(theta) - 1 = 0:
cos(theta) = 1
This value of cosine corresponds to the angle 0 degrees.
So, the possible solutions for theta in the given range are 180 degrees and 0 degrees.