Let (-4,-7) be a point on the terminal side of theta. Find the exact values of sin theta csc theta and cot theta

Question

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Answer 1

Here is a Youtube link to help explain the problem for you. Sadly we don't have anyway of drawing the solution out for you. It is important that you understand it, because it will follow you for the rest of trig.

 

https://www.youtube.com/watch?v=cNjzynK5QqE

Answer 2

 

The angle is in the 3rd quadrant where the tangent is positive. Consequently the cotangent is positive.

The sine is negative, so the cosecant is also negative.

 

With respect to the angle, the adjacent is -4 and the opposite is -7.

 

So the tangent is -7/-4 = 7/4 = 1.75

the angle is the inverse-tangent of 1.75 = 60.255.

So the actual angle is 240.255

The sine is -sqrt(3)/2

 

The cosecant is -2/sqrt(3) = -2*sqrt(3)/3 = (-2/3)*sqrt(3)

Answer 3

All problems of this type can be solved by making a drawing involving the described angle, including the reference triangle, which appears in the THIRD quadrant.  tan θ = 7/4 and you can solve for the hypotenuse of the reference triangle, namely √65. Then the rest of the trig function of this angle are easy. 

Egregious error corrected (quadrant 3). Thanks, Andy.