Question

Find the exact value of tan(cos^-1(-4/5))

Answer 1

need help please

Answer 2

\(\bf tan\left(cos^{-1}\left(-\frac{4}{5}\right)\right)\\
\color{blue}{cos^{-1}\left(-\frac{4}{5}\right) = \theta \implies cos(\theta) = -\cfrac{4}{5} \implies \cfrac{a}{c}\\
c^2= a^2+b^2 \implies \sqrt{c^2-a^2} = b}\\
tan\left(cos^{-1}\left(-\frac{4}{5}\right)\right) \implies tan(\theta) \implies \cfrac{b}{a}\)

Answer 3

I was thinking on what quadrant the angle is, but ..... we only know that a = -4
but that could be the 2nd and 3rd quadrants

so I gather there are 2 answers to the tangent function

Answer 4

ahaa

Answer 5

ahaa

Answer 6

ammm okey so is the first answer -3/4 ?

Answer 7

more like \(\bf \pm \cfrac{3}{4}\)

Answer 8

hhmmmm and r u sure about it?

Answer 9

you see the pythagorean theorem doesn't tell you if a root is either positive or negative, that will depend on the context
in this case the context is, we have an angle whose cosine is negative
any angle on the 2nd Quadrant will have a negative cosine
any angle on the 3rd Quadrant will have a negative cosine also

previously you knew where the angle was, so you knew what sign "b" will be

Answer 10

so you see, the cosine for those 2 angles is equally -4/5

Answer 11

i did it the right answer is -3/4 it's correct (((:

Answer 12

Thank you very much jdoe i learned a lot from you ^^

Answer 13

yw