What is theta in two cos theta squared minus cos theta equals one?

Answer 1

It's an equation that's sitting there begging us to find what values for Θ make it

a true statement.

For the first few moments, just to make it simpler to look at and to write, I'll

call cos(Θ) by the name 'C'.

You said that [ 2C2 - C = 1 ]

Subtract 1 from each side: [ 2C2 - C - 1 = 0 ]

This is a plain old quadratic equation.

When you factor it, it becomes . . . . . . (2C + 1) (C- 1) = 0

Setting each factor to zero in turn, you get the two roots:

C = 1

C = - 1/2

Now we can go back to the trig world:

cos(Θ) = C

cos(Θ) = 1 . . . . . Θ = any positive or negative multiple of 360° .

cos(Θ) = - 1/2 . . . Θ = (any positive or negative multiple of 360°) plus or minus 120° .