Find the angle θ such that 2θ + sin θ = cos θ

Question

In this problem angle theta must be greater than 0 and lesses than 2 pi

Answer 1

This problem mixes up apples and oranges

an angle is in radians or degrees while sines & cosines are pure unitless numbers

But ignoring that little problem, rewrite the equation as 2x = cosx - sinx

cosx - sinx tends to be less than 1

If 2x < 1, then x < 1/2 radian or less than 30 degrees

It's a relatively small angle, for small angles sinx = about x and cosx = about 1

2x + x = 1

3x = 1

x = 1/3 radian or less than 20 degrees

0.33 radians is an approximation

check either side of .33 and .32 radians appears closest for 2 decimal places