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# simple, yet I don't get it

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Hi There,

I was hoping someone could show me the working to the below.

I feel i'm missing something quite simple.

Aug 21, 2018

#1
+99301
+3

Hi Vest4R,

$$3Tcos\theta - 1.5Tsin\theta = 0\\ T(3cos\theta - 1.5sin\theta )= 0\\ T=0\;\;or\;\; 3cos\theta - 1.5sin\theta=0\\ T=0\;\;or\;\; 3cos\theta = 1.5sin\theta\\ T=0\;\;or\;\; \frac{3cos\theta}{1.5cos\theta} = \frac{1.5sin\theta}{1.5cos\theta }\\ T=0\;\;or\;\; 2 = tan\theta\\ T=0\;\;or\;\; tan\theta=2\\ T=0\;\;or\;\; \theta=atan(2)\qquad\;\;NOTE: \theta\text{ must be in the first or third quad}\\ T=0\;\;or\;\; \theta=(63.43+180n)^\circ \qquad where \qquad n\in Z$$

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Aug 21, 2018
#2
+203
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Thanks Melody,

Can I ask where: $$\frac{3cos\theta}{1.5cos\theta} = \frac{1.5sin\theta}{1.5cos\theta}$$ came from?

is this just dividing the left hand side by only half of its self?

Aug 21, 2018
#3
+203
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Actually, I just realized how silly I've been for the past couple of hours trying to work this out.....

$$3Tcos\theta - 1.5Tsin\theta = 0 \\ 3Tcos\theta =1.5Tsin\theta \\ 3T = 1.5T tan\theta \\ \frac{3}{1.5} = tan\theta$$

I appreciate your help for waking me up!!

Aug 21, 2018