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LeahM · Mar 26, 2007, 04:59 PM

I've got a take home test and only 3 hours left to do it, I'm not creative at all when it comes to trig identities, please prove this one

tan theta + cot theta = (sec theta)(csc theta)

also,

"find sin(theta+phi)

cos theta = -1/5 and sin phi = 3/5, with both angles in quadrant 2!

galactus · Mar 26, 2007, 05:38 PM

[QUOTE=LeahM]I've got a take home test and only 3 hours left to do it, I'm not creative at all when it comes to trig identities, please prove this one

$tan{\theta} + cot{\theta} = (sec{\theta})(csc{\theta})$

Rewrite as:

$\frac{sin{\theta}}{cos{\theta}}+\frac{cos{\theta}} {sin{\theta}}$

Cross-multiply:

$\frac{\overbrace{sin^{2}{\theta}+cos^{2}{\theta}}^ {\text{this equals 1}}}{cos{\theta}sin{\theta}}$

$\frac{1}{cos{\theta}}\cdot\frac{1}{sin{\theta}}=se c{\theta}csc{\theta}$

galactus · Mar 27, 2007, 10:42 AM

"find sin(theta+phi)

cos theta = -1/5 and sin phi = 3/5, with both angles in quadrant 2!

${\theta}=cos^{-1}(\frac{-1}{5})=sin^{-1}(\frac{1}{5})+\frac{\pi}{2}\approx{1.772154}, \;\ about \;\ 101.54 \;\ degrees.$

${\phi}=sin^{-1}(\frac{3}{5})\approx{0.6425011}, \;\ about \;\ 36.87 \;\ degrees.$

Use these to find $sin({\theta}+{\phi})$

Remember, you're in the 2nd quadrant.