1. ## Trig Functions (easy)

Hello, I need help with this equation

Solve $\cos (\Theta) = \sqrt{2}/2$ 0 $\leq \Theta$ < 2 $\pi$

And I'm told to Give exact answers. Use fractions, if necessary

Whoops a little LaTex error, now fixed.

2. The range of 0 to 2pi means an entire circle...so can you figure out what angle in 360 degrees has cos = $2\sqrt{2}$?

Hint... cos = adjacent over hypotenuse, so at what angles on the unit circle is the adjacent angle 2 and the hypotenuse $\sqrt{2}$?

3. There was a LaTex error that I had to fix, but with the new equation the angle is 45 degrees. So, would it be pi/4, 3pi/4, 5pi/4, and 7pi/4??

4. Originally Posted by OVechkin8
There was a LaTex error that I had to fix, but with the new equation the angle is 45 degrees. So, would it be pi/4, 3pi/4, 5pi/4, and 7pi/4??
Regarding your answer, not quite... according to your equation, the cos of theta is positive, so it can't be in all 4 quadrants. Cosine is only positive in quadrants I and IV. However, the reference angle is 45 degrees (or pi/4) so you've got the right answers in there. It's pi/4 and 7pi/4.

5. hm, ok I got it.

6. Originally Posted by OVechkin8
Hello, I need help with this equation

Solve $\cos (\Theta) = \sqrt{2}/2$ 0 $\leq \Theta$ < 2 $\pi$

And I'm told to Give exact answers. Use fractions, if necessary

Whoops a little LaTex error, now fixed.
nothing to "solve" here ... it's just knowledge of the unit circle.

$\cos{\theta} = \frac{\sqrt{2}}{2}$

$\theta = \frac{\pi}{4} \, , \, \frac{7\pi}{4}$