Thread: Using a sum or difference identity

1. Using a sum or difference identity

Question:
Find exact Value: Sin(15o).

So I know I can use Sin(45o - 30o) which would be (SinA)(SinB) - (CosA)(CosB): ((sqrt(2)/2)(1/2)) - ((sqrt(2)/2)(sqrt(3)/2)). I get the result: (sqrt(2)-sqrt(6))/4 . But the answer in the answer key is similar, but not this answer. At first it seems undistributed, but after making the attempt to do so, there is a negative in the wrong place. Answer Key: (sqrt(2)(sqrt(3)-1)/4.

Can someone point out my error? Or if I'm taking the wrong approach to this.

2. Re: Using a sum or difference identity

Find the exact value: $\displaystyle \sin(15^o)$

The identity is: .$\displaystyle \sin(A-B) \:=\:\sin A\cos B - \cos A\sin B$

$\displaystyle \sin(15) \;=\;\sin(45-30)$

. . . . . $\displaystyle =\;\sin45\cos30 - \cos45\sin30$

. . . . . $\displaystyle =\;\left(\frac{\sqrt{2}}{2}\right)\left(\frac{ \sqrt{3}}{2}\right) - \left(\frac{\sqrt{2}}{2}\right)\left(\frac{1}{2} \right)$

. . . . . $\displaystyle =\;\frac{\sqrt{2}(\sqrt{3}-1)}{4}$

3. Re: Using a sum or difference identity

Oh, great catch. What can I do to post this as solved? And for future reference how did you get the nice images for the fractions?

4. Re: Using a sum or difference identity

Click Reply With Quote to see what Soroban posted. Then you can see how he formatted his response.