Trig

**Colin_m** · March 31st 2008, 03:26 AM

Could someone please show me how to do these step by step please

a) Find the values of thita in the interval 0<theta<360 for which

sin(theta)tan(theta)-cos(theta)=1

b) Find in terms of pie, the values of x in the interval 0<x<2(pie) for which

3tanx-2cosx=0

**mr fantastic** · March 31st 2008, 03:52 AM

Originally Posted by Colin_m

Could someone please show me how to do these step by step please

a) Find the values of thita in the interval 0<theta<360 for which

sin(theta)tan(theta)-cos(theta)=1

b) Find in terms of pie, the values of x in the interval 0<x<2(pie) for which

3tanx-2cosx=0

Because I'm lazy, let $t = \theta$ .

a) $\Rightarrow \frac{\sin^2 t}{\cos t} - \cos t = 1$

$\Rightarrow \sin^2 t - \cos^2 t = \cos t$

$\Rightarrow (1 - \cos^2 t) - \cos^2 t = \cos t$

$\Rightarrow 2 \cos^2 t + \cos t - 1 = 0$

$\Rightarrow (2 \cos^2 - 1)(\cos t + 1) = 0$ .

All blue sky from here.

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b) $\Rightarrow \frac{3 \sin x}{\cos x} -2 \cos x=0$

$\Rightarrow 3 \sin x - 2 \cos^2 x = 0$

$\Rightarrow 3 \sin x - 2 (1 - \sin^2 x) = 0$

$\Rightarrow 3 \sin x - 2 + 2 \sin^2 x = 0$

$\Rightarrow 2 \sin^2 x + 3 \sin x - 2 = 0$

$\Rightarrow (2 \sin x - 1)(\sin x + 2) = 0$ .

All blue sky from here.

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