SOLUTION: 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

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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:



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:



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:



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:



John

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