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:
Three points determine a plane
Step-by-step explanation:
Answer:
Store B is offering the better deal on ground beef
Step-by-step explanation:
Dean is comparing prices on ground beef
Store A is selling 5 pounds of ground beef for $23.49
Store B is selling 8 pounds of ground beef for $36.96
We need to know which store is offering the better deal on ground beef
To find the better deal we must to find the unit price of each store
The unit price = total price ÷ number of pounds
∵ Store A is selling 5 pounds of ground beef for $23.49
∴ The unit price of Store A = 23.49 ÷ 5 = $4.698
∴ The unit price of Store A is $4.698 per pound
∵ Store B is selling 8 pounds of ground beef for $36.96
∴ The unit price of Store B = 36.96 ÷ 8 = $4.620
∴ The unit price of Store B is $4.620 per pound
∵ $4.620 < $4.698
∴ The unit price of Store B is less than the unit price of Store B
∴ Store B is cheaper than Store A, then it is offering the better deal
Answer:
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