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- Mar 16th 2008, 04:07 PM #1

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- Dec 2007
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## Triganometry , Help please

Hi, could someone tell what what i need to do to answer these q's please, thank you

All the angles are in interval -180degrees to 180degrees.

So , given that sina<0 and cos a =0.5 find a.

Im not sure what to do, so any help is great thank you all.

- Mar 16th 2008, 05:37 PM #2

- Mar 16th 2008, 05:49 PM #3
First we need to find a reference angle. To do this, find .

Recall the special triangle with sides 1, 2, and .

Where n is equal to any number. In this case, n is 1.

Cosine is equal to adjacent over hypotenuse, so in this case:

The adjacent side must be 1 and the hypotenuse must be 2. What angle in this triangle represents that? The 60 degree angle, or in radians.

So, is equal to .

Now that we have our reference angle, think about the quadrants. We know that is less than zero and therefore negative, so which quadrants are negative in? The third and fourth quadrants.

Recall that sin is a periodic function, repeating every .

So, the values of a that satisfy this equation are:

, where n is any integer.

For which values of n does this equation fall into the third or fourth quadrant? The only correct answer is 1.

So, your final answer is: