# solving trig equations

• Feb 17th 2010, 02:28 PM
paramorechick99
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:D
• Feb 17th 2010, 02:38 PM
pickslides
Quote:

Originally Posted by paramorechick99

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

Are you allowed to use a calculator?

if not consider,

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

Now apply the rules

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

and

$\sin(a) = \sqrt{\frac{1-\cos(a)}{2}}$ and $\cos(a) = \sqrt{\frac{1+\cos(a)}{2}}$
• Feb 17th 2010, 02:51 PM
skeeter
Quote:

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:D

the three sum difference formulas ...

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

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

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

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

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

plug and chug.

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

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

$-\sin{x} = 1
$

$\sin{x} = -1$

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

you do the second one.