sum/difference/half angle formula

**lsnyder** · April 13th 2009, 12:32 PM

I do not understand what to do for these problems. I am very lost can someone show me how to do one of these.

And I copied and pasted my homework on here so I didnt mess up the instructions or problem(s).

Use a sum or difference formula or a half angle formula to determine the value of the trigonometric functions. Give exact answers. Do not use decimal numbers. The answer should be a fraction or an arithmetic expression. If the answer involves a square root it should be enter as sqrt; e.g. the square root of 2 should be written as sqrt(2);

=

**icemanfan** · April 13th 2009, 12:40 PM

Originally Posted by lsnyder

I do not understand what to do for these problems. I am very lost can someone show me how to do one of these.

And I copied and pasted my homework on here so I didnt mess up the instructions or problem(s).

Use a sum or difference formula or a half angle formula to determine the value of the trigonometric functions. Give exact answers. Do not use decimal numbers. The answer should be a fraction or an arithmetic expression. If the answer involves a square root it should be enter as sqrt; e.g. the square root of 2 should be written as sqrt(2);

=

The easiest one is the third. Use $\cos (\frac{1}{2}\theta) = \sqrt{\frac{\cos \theta + 1}{2}}$ with $\theta = \frac{\pi}{4}$ .

**lsnyder** · April 13th 2009, 12:55 PM

um, I am still lost. Is there a way you can be more detailed or break it down more?

**icemanfan** · April 13th 2009, 01:43 PM

I gave you the half-angle identity for cosine. You can use this identity to compute $\cos \frac{\pi}{8}$ as I indicated.

$\cos \frac{\pi}{8} = \sqrt{\frac{\cos \frac{\pi}{4} + 1}{2}}$

You know what $\cos \frac{\pi}{4}$ is so you can compute the answer.

**Jhevon** · April 13th 2009, 01:58 PM

Originally Posted by lsnyder

=

$\sin \left( \frac {-5 \pi}8\right) = - \sin \frac {5 \pi}8 = - \sin \left[ \frac 12 \left( \frac {5 \pi}4 \right) \right]$
.......... $\uparrow$
..reference angle

now use the half angle formula for sine.

=

$= - \sin \frac {7 \pi}{12}$ .......since sine is an odd function

$= - \sin \left( \frac {4 \pi}{12} + \frac {3 \pi}{12} \right)$

$= - \sin \left( \frac {\pi}3 + \frac {\pi}4 \right)$

now use the addition formula for sine

=

Icemanfan responded to this.

=

do a similar manipulation as i did with the first, and use the half angle formula for cosine.

WARNING: $\cos (-x) = \cos x$ since cosine is an even function. this makes an important difference in what i did in the first problem

**lsnyder** · April 13th 2009, 02:10 PM

Originally Posted by icemanfan

I gave you the half-angle identity for cosine. You can use this identity to compute $\cos \frac{\pi}{8}$ as I indicated.

$\cos \frac{\pi}{8} = \sqrt{\frac{\cos \frac{\pi}{4} + 1}{2}}$

You know what $\cos \frac{\pi}{4}$ is so you can compute the answer.

okay in corresponding to cos(pi/4) its sqrt(2)/2. but I keep typing that in and getting it wrong. so am i going about this wrong?

**lsnyder** · April 13th 2009, 02:12 PM

Also, I do not know the half-angle formula. So am I lost when it comes to that formula. So what is the half-angle formula?

**Jhevon** · April 13th 2009, 02:26 PM

Originally Posted by lsnyder

Also, I do not know the half-angle formula. So am I lost when it comes to that formula. So what is the half-angle formula?

are you kidding? this is not something we have to tell you. i am sure the formula is in your text, and if you can't bother looking for it in there, you have internet access, typing "half angle formulas" into google is not that hard

**lsnyder** · April 13th 2009, 05:48 PM

Originally Posted by Jhevon

are you kidding? this is not something we have to tell you. i am sure the formula is in your text, and if you can't bother looking for it in there, you have internet access, typing "half angle formulas" into google is not that hard

I wouldn't have asked if I had not been looking for it. And I did type it in google, which only shows either double half angles(?) and examples. It doesn't explain how it works or is solved. & instead of wasting time to type that, you could of given me a reference or explaination. its more helping than telling.

**Jhevon** · April 13th 2009, 05:51 PM

Originally Posted by lsnyder

I wouldn't have asked if I had not been looking for it. And I did type it in google, which only shows either double half angles(?) and examples. It doesn't explain how it works or is solved. & instead of wasting time to type that, you could of given me a reference or explanation. its more helping than telling.

4. Half Angle Formulas ...it also shows how they are derived

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