1. ## solving trig equations

If anyone could help me out here it would be greatl appreciated.(:

find sin, cos, tan of:
255 degrees
17pi/12

find value of:
cos(x+ pi/6) - cos(x - pi/6)=1
sin(x+ pi/6) - sin(x - pi/6)=1/2

thank you sooo much

2. Originally Posted by paramorechick99

find sin, cos, tan of:
255 degrees
17pi/12
Are you allowed to use a calculator?

if not consider,

$\displaystyle \sin\left(\frac{17\pi}{12}\right) = \sin\left(\frac{12\pi}{12}+\frac{5\pi}{12}\right)$

Now apply the rules

$\displaystyle \sin(a+b) = \sin(a)\cos(b)+\sin(b)\cos(a)$

and

$\displaystyle \sin(a) = \sqrt{\frac{1-\cos(a)}{2}}$ and $\displaystyle \cos(a) = \sqrt{\frac{1+\cos(a)}{2}}$

3. Originally Posted by paramorechick99
If anyone could help me out here it would be greatl appreciated.(:

find sin, cos, tan of:
255 degrees
17pi/12

find value of:
cos(x+ pi/6) - cos(x - pi/6)=1
sin(x+ pi/6) - sin(x - pi/6)=1/2

thank you sooo much
the three sum difference formulas ...

$\displaystyle \cos(a \pm b) = \cos{a}\cos{b} \mp \sin{a}\sin{b}$

$\displaystyle \sin(a \pm b) = \sin{a}\cos{b} \pm \cos{a}\sin{b}$

$\displaystyle \tan(a \pm b) = \frac{\tan{a} \pm \tan{b}}{1 \mp \tan{a} \tan{b}}$

note that $\displaystyle 255 = (225+30)$ or $\displaystyle (300-45)$ ... unit circle values

$\displaystyle \frac{17\pi}{12} = \frac{5\pi}{3} - \frac{\pi}{4}$ or $\displaystyle \frac{3\pi}{4} + \frac{2\pi}{3}$ ... unit circle values

plug and chug.

$\displaystyle \cos\left(x + \frac{\pi}{6} \right) - \cos\left(x - \frac{\pi}{6} \right) = 1$

$\displaystyle \cos{x} \cdot \frac{\sqrt{3}}{2} - \sin{x} \cdot \frac{1}{2} - \left[\cos{x} \cdot \frac{\sqrt{3}}{2} + \sin{x} \cdot \frac{1}{2}\right] = 1$

$\displaystyle -\sin{x} = 1$

$\displaystyle \sin{x} = -1$

$\displaystyle x = \frac{3\pi}{2}$

you do the second one.