# Math Help - Trig

1. ## Trig

Can someone help me with these?

1. Simplify, listing reasons: cos^2 theta times csc theta + sin theta.

2. Given the stated information, sketch theta and find the exact values.
a. cos alpha(in degrees) = -1\2, 180 degrees < alpha < 360 degrees, find alpha, sin value and tan value.
b. If sin^-1 (squareroot of 3 over 2) = alpha^R ad alpha^R lies in quadrant II, find alpha^R, cos value and tan value.
c. tan alpha^R = -1/root3, pi < alpha < 2pi, find alpha, sex value, and csc value
d. sin alpha(in degrees) = 0, 90 degrees < or = to alpha < or = to 270 degrees, find alpha, cos value and tan value.
e. sec alpha^R = root 2, pi < alpha < 2pi, find alpha, cot value and sin value

2. Originally Posted by jakej78
Can someone help me with these?
Sure, we can help. What have you tried, and where do you get stuck?

3. The first one, I don't even know where to start, considering I wasn't taught it, but was still given it.

The second one, I don't know how to start it, nor how to graph it. I just honestly don't get it, and I don't think I was taught it quite yet.. For a, I'm guessing you graph -1/2 (how though?) and I don't know what the 180 < alpha < 360 is?

4. Originally Posted by jakej78
The first one, I don't even know where to start, considering I wasn't taught it, but was still given it.

The second one, I don't know how to start it, nor how to graph it. I just honestly don't get it, and I don't think I was taught it quite yet.. For a, I'm guessing you graph -1/2 (how though?) and I don't know what the 180 < alpha < 360 is?
a) $\cos\alpha=-\frac{1}{2}$ means we are dealing with an angle in either $QII$ or $QIII$. Then $\alpha=\arccos(\frac{1}{2})=60^{\circ}$ implies that $\alpha=120^{\circ},240^{\circ}$ for $\alpha\in[0,360^{\circ}]$. But, we want $\alpha\in(180^{\circ},360^{\circ})$. Therefore, $\alpha=240^{\circ}$

5. Ohhh okay, I get that now.. makes such more sense!

I'm having trouble with
1. Simplify, listing reasons: cos^2 theta times csc theta + sin theta.
b. If sin^-1 (squareroot of 3 over 2) = alpha^R and alpha^R lies in quadrant II, find alpha^R, cos value and tan value.

Can you help me with those?

6. Originally Posted by jakej78
Ohhh okay, I get that now.. makes such more sense!

I'm having trouble with
1. Simplify, listing reasons: cos^2 theta times csc theta + sin theta.
b. If sin^-1 (squareroot of 3 over 2) = alpha^R and alpha^R lies in quadrant II, find alpha^R, cos value and tan value.

Can you help me with those?
is #1. $\cos^2\theta\csc\theta+\sin\theta$ or $\cos^2\theta(\csc\theta+\sin\theta)$?
Let's say its the first...

$\cos^2\theta\csc\theta+\sin\theta=\cos^2\theta\fra c{1}{\sin\theta}+\sin\theta=\cot\theta\cos\theta+\ sin\theta$

7. its cos^2 theta times(as in multiplying.. the dot) csc theta + sin theta.

8. Originally Posted by jakej78
its cos^2 theta times(as in multiplying.. the dot) csc theta + sin theta.
so...the second one then?

or is it

$\cos^2[\theta(\csc\theta+\sin\theta)]$.

Do you know how to input commands into a graphing calculator? If so, just go ahead and type it out just like that. I'll understand what you mean.

9. $
\cos^2\theta\bullet\csc\theta+\sin\theta
$

would be it..