Question 1123120: Given tan θ = -5/12 and cos θ > 0, find csc θ. Write your answer as a fraction.
Found 2 solutions by josgarithmetic, Theo:
Answer by josgarithmetic(39630)   (Show Source):
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! the problem is:
Given tan theta = -5/12 and cos theta > 0, find csc theta.
tangent is negative in the second and fourth quadrant.
cosine is positive in the first and fourth quadrant.
therefore, if tangent is negative and cosine is positive, the angle has to be in the fourth quadrant.
cosecant is the reciprocal of sine.
sine is negative in the fourth quadrant.
cosecant is the reciprocal of sine, therefore cosecant will also be negative in the fourth quadrant.
form your triangle in the fourth quadrant as shown in the following diagram.
your solution is that csc(A) = 13/-5
in the diagram, angle A is equal to theta.
i should have put there, but forgot.
here's a reference on angles in different quadrants you might find useful.
https://www.purplemath.com/modules/quadangs.htm
the hypotenuse of the right triangle is always positive, regardless of what quadrant the angle is in.
note that csc theta = 1 / sin theta = 1 / (a/c) = 1 * (c/a) = c/a = 13/-5.
wherever you see trig function (A), you can translate that to trig function (theta).
|
|
|
