- #1
johnstobbart
- 22
- 0
Homework Statement
My trig is really rusty and I've been trying to figure out why the answer is what it is:
Find all solutions of the following equation:
sin2 x + cos x - 1.
Homework Equations
Just the identity:
sin2 θ + cos2 θ = 1
The Attempt at a Solution
The sin2 x is in the way, so I substitute 1 - cos2 x in it's place to get:
(1 - cos2 x + cos x - 1 = 0
The ones are removed and cos x is common, so:
cos x(-cos x + 1) = 0
This means that:
cos x = 0 or cos x = -1
From the unit circle, we get:
cos x = ∏/2 or cos = ∏
Here is where I get confused:
I know we need to make this true for all intervals so:
cos x = 0 whenever x = ± ∏/2 + 2k∏ or,
cos x = -1 whenever x = ± ∏ + 2k∏ for any integer k.
That's my final answer. According to my textbook, It's wrong, but I have no idea why. The textbook gives the final answer as:
cos x = 0 whenever x = ∏/2 + 2k∏ or,
cos x = -1 whenever x = ∏ + 2k∏ for any integer k.
Is it wrong that x = ± ∏/2 or x = ±∏?