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**rtblue** Hey guys, I have a pretty botchy understanding of trigonomety. My class has not started trigonometry yet, but I was interested so I tried to learn some. The question I have is this:

$\displaystyle Evaluate: \sin(\frac{\pi}{4}) - \cos(\frac{\pi}{3})+\tan(\frac{3\pi}{4})-\csc(\frac{5\pi}{4})+\sec(\frac{4\pi}{3})$

My Attempt:

1. I see that the first term(sine of 45) will be $\displaystyle \displaystyle \frac{\sqrt{2}}{2}$

2. I see that the second term(cosine of 60) will be $\displaystyle \displaysyle\frac{1}{2}$

3. Now, I get a bit confused. I realize that the third term is the tangent of 135. I kind of took a stab at this and said that it was -tan45 (this is purely guesswork). That gave me -1.

4. And the confusion grows. I evaluate the fourth term as 1/sin(225). I'm pretty sure sin225= -sin45, and so this gave me $\displaystyle \displaysyle -\sqrt{2}$.

5. So i take the fifth term as 1/cos(240), which i think is 1/-cos60. I get this to equal -2.

Once I compile all of this, I get $\displaystyle \displaystyle \frac{3\sqrt{2}-7}{2}$

This is one of the answer choices, but I'm not sure if I messed up somewhere. Any help is appreciated.

And one quick side question:

Is tan(x)= -tan(180-x)?

Thank you for any help.