Question

Find cos θ if sin θ =-12/13 and tan θ > 0

Answer 1

\(\bf sin(\theta) = -\cfrac{12}{13} \implies \cfrac{\textit{opposite side}}{\textit{hypotenuse}} \implies \cfrac{b}{c}\\
\textit{keep in mind that}\\
c^2 = a^2+b^2 \implies \sqrt{c^2-b^2} = a^2\\
\textit{if } tan(\theta) > 0\\
tan(\theta) = \cfrac{\textit{opposite side}}{\textit{adjacent side}}\implies\cfrac{b}{a}\\
sin(\theta) \textit{ is negative, thus }cos(\theta) \textit{ is also negative}\)

Answer 2

there are 2 ways to go about this...
i will show 1 way which is using formula
\[\sin^{2}x + \cos^{2}x = 1\]
...oh nevermind

Answer 3

Okay, so then you just plug in the sides?

Answer 4

its a 3rd quadrant angle, tan > 0 sin <0

draw a picture



find x using pythagoras' theorem

and it will be negative because of its location on the number plane.

then you can find cos