Question

If cos Θ = negative 4 over 7, what are the values of sin Θ and tan Θ? (2 points)

Answer 1

I accept that θ in second quadrant, therefore sinθ > 0, cosθ < 0 and tanθ < 0.


`\cos\theta=-(4)/(7)\\\\We\ know:\sin^2x+\cos^2x=1\to\sin^2x=1-\cos^2x\to\sin x=√(1-\cos^2x)\\\\subtitute:\\\\\sin x=\sqrt{1-\left(-(4)/(7)\right)^2}=\sqrt{1-(16)/(49)}=\sqrt{(33)/(49)}=(√(33))/(7)`


`We\ know:\tan x=(\sin x)/(\cos x)\\\\subtitute:\\\\\tan x=(√(33))/(7):\left(-(4)/(7)\right)=-(√(33))/(7)\cdot(7)/(4)=-(√(33))/(4)`