You have 22 friends to invite to your birthday party, let n represent the number of friends that couldn't make it. At the party, only 15 of my friends came. How many friends didn't come to your birthday party?
Answer:
6
Step-by-step explanation:
X/126=1/21
X=126/21
X=6
is it right?
Answer:
![\tan(\theta)=\frac{-\sqrt{5}}{2}](https://tex.z-dn.net/?f=%5Ctan%28%5Ctheta%29%3D%5Cfrac%7B-%5Csqrt%7B5%7D%7D%7B2%7D)
Step-by-step explanation:
Since we are in quadrant 2, sine is positive. Since sine is positive and cosine is negative, then tangent is negative.
Now I'm going to find the sine value of this angle given using one of the Pythagorean Identities, namely
.
If given
, then we have
by substitution of
.
Let's solve:
for
.
![\sin^2(\theta)+\frac{4}{9}=1](https://tex.z-dn.net/?f=%5Csin%5E2%28%5Ctheta%29%2B%5Cfrac%7B4%7D%7B9%7D%3D1)
Subtract 4/9 on both sides:
![\sin^2(\theta)=1-\frac{4}{9}](https://tex.z-dn.net/?f=%5Csin%5E2%28%5Ctheta%29%3D1-%5Cfrac%7B4%7D%7B9%7D)
Simplify:
![\sin^2(\theta)=\frac{5}{9}](https://tex.z-dn.net/?f=%5Csin%5E2%28%5Ctheta%29%3D%5Cfrac%7B5%7D%7B9%7D)
Square root both sides:
![\sin(\theta)=\sqrt{\frac{5}{9}}](https://tex.z-dn.net/?f=%5Csin%28%5Ctheta%29%3D%5Csqrt%7B%5Cfrac%7B5%7D%7B9%7D%7D)
![\sin(\theta)=\frac{\sqrt{5}}{\sqrt{9}}](https://tex.z-dn.net/?f=%5Csin%28%5Ctheta%29%3D%5Cfrac%7B%5Csqrt%7B5%7D%7D%7B%5Csqrt%7B9%7D%7D)
![\sin(\theta)=\frac{\sqrt{5}}{3}](https://tex.z-dn.net/?f=%5Csin%28%5Ctheta%29%3D%5Cfrac%7B%5Csqrt%7B5%7D%7D%7B3%7D)
===========
![\tan(\theta)=\frac{\sin(\theta)}{\cos(\theta)}=\frac{\frac{\sqrt{5}}{3}}{\frac{-2}{3}}](https://tex.z-dn.net/?f=%5Ctan%28%5Ctheta%29%3D%5Cfrac%7B%5Csin%28%5Ctheta%29%7D%7B%5Ccos%28%5Ctheta%29%7D%3D%5Cfrac%7B%5Cfrac%7B%5Csqrt%7B5%7D%7D%7B3%7D%7D%7B%5Cfrac%7B-2%7D%7B3%7D%7D)
Multiplying top and bottom by 3 gives:
![\tan(\theta)=\frac{\sqrt{5}}{-2}](https://tex.z-dn.net/?f=%5Ctan%28%5Ctheta%29%3D%5Cfrac%7B%5Csqrt%7B5%7D%7D%7B-2%7D)
I'm going to move the factor of -1 to the top:
![\tan(\theta)=\frac{-\sqrt{5}}{2}](https://tex.z-dn.net/?f=%5Ctan%28%5Ctheta%29%3D%5Cfrac%7B-%5Csqrt%7B5%7D%7D%7B2%7D)
Answer:
6
Step-by-step explanation:
6