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.

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- Mar 16th 2008, 03:07 PM #1

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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, 04:37 PM #2

- Mar 16th 2008, 04:49 PM #3
First we need to find a reference angle. To do this, find $\displaystyle cos \frac {1}{2}$.

Recall the special triangle with sides 1, 2, and $\displaystyle \sqrt {3}$.

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

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

$\displaystyle cos \frac {1}{2}$

The adjacent side must be 1 and the hypotenuse must be 2. What angle in this triangle represents that? The 60 degree angle, or $\displaystyle \frac {\pi}{3}$ in radians.

So, $\displaystyle cos \frac {1}{2}$ is equal to $\displaystyle \frac {\pi}{3}$.

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

Recall that sin is a periodic function, repeating every $\displaystyle 2\pi$.

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

$\displaystyle 2n\pi + \frac {\pi}{3}$, 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:

$\displaystyle 2\pi + \frac {\pi}{3}$

$\displaystyle = \frac {7\pi}{3}$