Question

Use the fundamental identities to find the calculate of the trig function

Answer 1

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

Answer 2

\(\bf tan(\theta)>0\) simply means, the tangent is positive

\(\bf {\color{brown}{ sin}}(\theta)=\cfrac{opposite}{hypotenuse}
=\cfrac{y}{r}\impliedby -\cfrac{12}{13}
\\ \quad \\
\textit{"r" radius, is always positive, thus }\implies \cfrac{-12=y}{13=r}\)

Answer 3

hmmm

Answer 4

hold off.. there... that tangent there is ... negative... so... can't be on that quadrant

Answer 5

anyhow... tangent is positive in 3rd and 1st quadrants
y = -12, that means, 3rd quadrant

Answer 6

sigh you got the easy trig :/

Answer 7

so... to use the pythagorean theorem
we know the opposite side, -12
we know the hypotenuse, 13
to find the adjacent side, we'd just use that then,

\(\bf c^2=a^2+b^2\implies hypotenuse^2=adjacent^2+opposite^2
\\ \quad \\
13^2=a^2+(-12)^2\implies 13^2-(-12)^2=a^2
\\ \quad \\
\pm\sqrt{13^2-(-12)^2}=a\)

we know the tangent is positive
"y" is negative
tangent = y/x

to get a positive tangent, "x" must also be negative
we also know anyway, that "x" is negative on the 3rd Quadrant, thus
\(\large \bf -\sqrt{13^2-(-12)^2}=a\)

Answer 8

Okay so I understand what you are saying, I used the Pythagorean identity (sin^2 x + cos^2 x = 1) and found that cos equals -5/13

Answer 9

yeap... you could use that as well, yes

Answer 10

alright sweet! thanks man!

Answer 11

yw