Question 509195: Evaluate:
Sec (-7pi/6) + Csc (pi/3) + tan 8pi/3
This is what I have so far:
Sec -210 = -2 times the square root of 3 / 3
Csc 30 = 2
tan 480 = - the square root of 3
What I got was -5 times the square root of 3 + 6.
How do you get a - square root of 3?
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
Let's look at the unit circle:
Note that 
And recall that 
So, find  on the unit circle, note that the  -coordinate is  , take the reciprocal and rationalize to get:
\ =\ -\frac{2\sqrt{3}}{3})
Which is what you had.
Now, recall that 
So, find  on the unit circle, note that the  -coordinate is  , take the reciprocal and rationalize to get:
\ =\ \frac{2\sqrt{3}}{3})
Hence the sum of your first two terms is zero.
Now for the third term:
Note that 
Since the tangent function has a periodicity of  , we can conclude that:
\ =\ \tan\left(\frac{2\pi}{3}\right))
Now, recall that 
So, find  on the unit circle, note that the -coordinate is , the -coordinate is  , and then take the quotient of the -coordinate divided by the -coordinate to get:
\ =\ \frac{\frac{\sqrt{3}}{2}}{-\frac{1}{2}}\ =\ -\sqrt{3})
John
My calculator said it, I believe it, that settles it
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