Given cosθ=–1/5 and tan θ 0, find sin θ.

Question

Given cosθ=–1/5 and tan θ > 0, find sin θ.

anonymous · Answer

as tan theta >0, sin theta must be less than 0
so cos^2 +sin^2 =1
sin^2 theta=1-1/25= 24/2
$$\sin \theta = 2\sqrt6/5$$

anonymous · Answer

sorry, it will be negative

anonymous · Answer

$$-2\sqrt{6}/5$$

imstuck · Answer

OMG you poor guy.  I drew it out to make it easier.  Tangent is positive in quadrants 1 and 3.

imstuck · Answer

If your cosine is negative, it is negative in 2 and 3.  The common quadrant here is 3 so the angle exists in Q3.|dw:1402331295308:dw|

imstuck · Answer

What is the sin of that angle?  Sin is opposite over hypotenuse.  The side opposite is -sqrt24 and the hypotenuse is 5.  So $$\sin \theta=\frac{ -\sqrt{24} }{ 5 }$$

imstuck · Answer

See that?  Draw it out.  It makes it so much easier.

anonymous · Answer

thank you!!

imstuck · Answer

Arnab09 did it the same way, but if you struggle with this, I find it easier to draw out the triangle and in the correct quadrant.  At least that is the way I had to teach my Trig kids how to figure these out!