(x-1)(x^2-2)/(x-1)(x-3) sorry if i’m wrong but im pretty sure im right
Since
lies in quadrant II and
lies in quadrant IV, we expect
,
, and
.
Recall the Pythagorean identities,
![\sin^2x+\cos^2x=1\iff1+\cot^2x=\csc^2x\iff\tan^2x+1=\sec^2x](https://tex.z-dn.net/?f=%5Csin%5E2x%2B%5Ccos%5E2x%3D1%5Ciff1%2B%5Ccot%5E2x%3D%5Ccsc%5E2x%5Ciff%5Ctan%5E2x%2B1%3D%5Csec%5E2x)
It follows that
![\sec\alpha=\dfrac1{\cos\alpha}=-\sqrt{\tan^2\alpha+1}=-\dfrac{13}5\implies\cos\alpha=-\dfrac5{13}](https://tex.z-dn.net/?f=%5Csec%5Calpha%3D%5Cdfrac1%7B%5Ccos%5Calpha%7D%3D-%5Csqrt%7B%5Ctan%5E2%5Calpha%2B1%7D%3D-%5Cdfrac%7B13%7D5%5Cimplies%5Ccos%5Calpha%3D-%5Cdfrac5%7B13%7D)
![\sin\alpha=\sqrt{1-\cos^2\alpha}=\dfrac{12}{13}](https://tex.z-dn.net/?f=%5Csin%5Calpha%3D%5Csqrt%7B1-%5Ccos%5E2%5Calpha%7D%3D%5Cdfrac%7B12%7D%7B13%7D)
![\sin\beta=-\sqrt{1-\cos^2\beta}=-\dfrac45](https://tex.z-dn.net/?f=%5Csin%5Cbeta%3D-%5Csqrt%7B1-%5Ccos%5E2%5Cbeta%7D%3D-%5Cdfrac45)
Recall the angle sum identity for sine:
![\sin(\alpha+\beta)=\sin\alpha\cos\beta+\sin\beta\cos\alpha](https://tex.z-dn.net/?f=%5Csin%28%5Calpha%2B%5Cbeta%29%3D%5Csin%5Calpha%5Ccos%5Cbeta%2B%5Csin%5Cbeta%5Ccos%5Calpha)
So we have
![\sin(\alpha+\beta)=\dfrac{12}{13}\dfrac35+\left(-\dfrac45\right)\left(-\dfrac5{13}\right)=\boxed{\dfrac{56}{65}}](https://tex.z-dn.net/?f=%5Csin%28%5Calpha%2B%5Cbeta%29%3D%5Cdfrac%7B12%7D%7B13%7D%5Cdfrac35%2B%5Cleft%28-%5Cdfrac45%5Cright%29%5Cleft%28-%5Cdfrac5%7B13%7D%5Cright%29%3D%5Cboxed%7B%5Cdfrac%7B56%7D%7B65%7D%7D)
This look overly complicated I think it’s just 136 because 180 - 46 is 136
I'm guessing that you don't really want the formulas. I think what you actually want
is the definitions of those functions of an acute angle when it's in a right triangle.
Cosine = (adjacent side) / (hypotenuse)
Tangent = (opposite side) / (adjacent side)
Sine = (opposite side) / (hypotenuse)
Tell me if I'm wrong, and I'll find some formulas for you.
Simplify 3.8x + 5.2x - 6.7 to 9x - 6.7
9x - 6.7 = 11.3
Add 6.7 to both sides
9x = 11.3 + 6.7
Simplify 11.3 + 6.7 to 18
9x = 18
Divide both sides by 9
x = 18/9
Simplify 18/9 to 2
<u>x = 2</u>