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# trig help

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Find sin θ if cot θ = - 2 and cos θ < 0.

Oct 24, 2015

#3
+10070
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I have made a small mistake.

Oct 24, 2015

#1
0

sin(theta) = -sin(cot^(-1)(2)-pi c1)

Oct 24, 2015
#2
+10070
+5

Hallo guest

Oct 24, 2015
#3
+10070
+5

I have made a small mistake.

Omi67 Oct 24, 2015
#4
+99272
+5

Find sin θ if cot θ = - 2 and cos θ < 0.

Thanks Omi for that great answer,

I have yet another method.

Since cos is negative the answer must be in the 2nd or third quad

Since cot is neg, tan is also neg so it is in the 2nd or  4th quad.

Therefore it is in the 2nd quad where sine is positive!

I am going to put that knowledge aside for a bit and work out the first quadrant equivalent.

$$cot\theta=\frac{2}{1}\\ so\\ tan\theta=\frac{1}{2}$$

Draw a right angled triangle and mark one angle as theta, then put

1 on the opposite side and

2 on the adjacent side so that tan theta = 1/2

Find the hypotenuse using pythagoras

$$hypotenuse=\sqrt{1^2+2^2}=\sqrt{5}$$

$$sin\theta = \frac{opp}{hyp}=\frac{1}{\sqrt5}=+\frac{\sqrt5}{5}$$

(positive for our final answer too because theta is in  the 2nd quad where sine is positive.)

At this point is is FINISHED.  You are not asked to find theta :))

so

Oct 25, 2015