if tan(theta) = -3/4 and cos(theta) 0. find other trig functions

Question

if tan(theta) = -3/4 and cos(theta) > 0. find other trig functions

imstuck · Answer

Where is the tangent function negative?  Do you know?

imstuck · Answer

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anonymous · Answer

when cos theta is negative then theta lies in 2nd quadrant

imstuck · Answer

However, they also tell you that cos theta is greater than 0.  So that is going to narrow it down.  Let's see where cos theta is positive.

imstuck · Answer

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imstuck · Answer

Tangent is negative in Q4 and cos is positive in Q4.  So we are Q4!  First problem solved!

imstuck · Answer

They tell you that the tangent of theta is -3/4, which is y/x in Q4.  Here's what it looks like in the plane.

imstuck · Answer

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imstuck · Answer

You need to solve for x in order to find the other functions.  Can you find x?

imstuck · Answer

Are you with me here?

anonymous · Answer

i literally am trying to answer a question from a module to pass a placement test. so I wasn't given that. That's what the question asked

anonymous · Answer

this is not that complicated
draw a right triangle |dw:1414113357509:dw|

anonymous · Answer

by pythagoras, this is the mother of all right triangles, a 3 - 4 - 5 right triangle|dw:1414113411066:dw|

anonymous · Answer

then you can find any trig ratio you like
you have to know that you area in quadrant 4 so that cosine is positive, sine is negative