trig equations please show all working especially part a (1 Viewer)

kpad5991 · Jan 15, 2017

a) cot theta = 0

b) 2 sin theta cos theta = sin theta

c) sec^2 x -2tan x -4 = 0

d) 6 tan^2 x = 5 sec x

pikachu975 · Jan 15, 2017

kpad5991 said:
a) cot theta = 0

b) 2 sin theta cos theta = sin theta

c) sec^2 x -2tan x -4 = 0

d) 6 tan^2 x = 5 sec x

a) cotx = 0 when tanx is infinity, so that is at pi/2 and 3pi/2 (Graph) assuming domain of 0 to 2pi since this is 2 unit.

InteGrand · Jan 15, 2017

kpad5991 said:
a) cot theta = 0

b) 2 sin theta cos theta = sin theta

c) sec^2 x -2tan x -4 = 0

d) 6 tan^2 x = 5 sec x

$\noindent a) Since $\cot \theta = \frac{\cos \theta}{\sin \theta}$, we have $\cot \theta = 0$ iff $\cos \theta = 0$, which is when $\theta = \frac{\pi}{2} + n\pi$, for some $n\in \mathbb{Z}$.$

$\noindent b) Either $\sin \theta = 0$ or $\cos \theta = \frac{1}{2}$. The former equation has solution $\theta = n\pi$ ($n\in \mathbb{Z}$) and the latter has solution $\theta = \pm \frac{\pi}{3}+2m\pi$ ($m\in \mathbb{Z}$), so these are the solutions.$

$\noindent c) Recall that $\sec^{2}x = \tan^{2}x + 1$, so the given equation becomes $\tan^{2}x-2\tan x -3 = 0$, i.e. $\left(\tan x -3\right)\left(\tan x + 1\right) = 0$, so the solutions are $x = \arctan (3) + m\pi$ or $x = -\frac{\pi}{4} + m\pi$ ($m\in \mathbb{Z}$).$

I'll leave part d) for you for now, it's similar to c).

trig equations please show all working especially part a (1 Viewer)

kpad5991

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pikachu975

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InteGrand

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