Question

Problems which I cannot for the life of me figure out why I got wrong/partially incorrect:

A: Find all six trigonometric functions of θ if the given point is on the terminal side of θ. (Assume that a is a positive number. If an answer is undefined, enter UNDEFINED.)
(−5a, −12a)
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B: Use your calculator to find sin θ and cos θ if the point (9.37, 7.05) is on the terminal side of θ. (Round your answers to four decimal places.)
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C: Indicate the quadrants in which the terminal side of θ must lie under the following conditions. (Select all that apply.)
cos θ and cot θ have the same sign
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Answer 1

So we get
\[\sin(\theta)=\sin(180+x)=-\sin(x)\]
\[\cos(\theta)=\cos(180+x)=-\cos(x)\]\[\tan(\theta)=\tan(180+x)=\tan(x)\]
from the triangle we can get
\[\sin(x)=\frac{-12a}{\sqrt{(-12a)^2+(-5a)^2}}=\frac{-12a}{\sqrt{144a^2+25a^2}}=\frac{-12a}{13a}=-\frac{12}{13}\]
Similarly find cos(x) and tan(x) and use them to find sin(theta), cos(theta) and tan(theta)
reciprocal for cosec(theta) sec(theta) and cot(theta)