Answer:
![cos(x)=\frac{\sqrt{5}}{5}](https://tex.z-dn.net/?f=cos%28x%29%3D%5Cfrac%7B%5Csqrt%7B5%7D%7D%7B5%7D)
Step-by-step explanation:
we have that
![tan(x)=-2](https://tex.z-dn.net/?f=tan%28x%29%3D-2)
The angle x is in quadrant IV
That means ---> The value of cos(x) is positive and the value of sin(x) is negative
Remember that
----> equation A
![tan(x)=\frac{sin(x)}{cos(x)}](https://tex.z-dn.net/?f=tan%28x%29%3D%5Cfrac%7Bsin%28x%29%7D%7Bcos%28x%29%7D)
so
![-2=\frac{sin(x)}{cos(x)}](https://tex.z-dn.net/?f=-2%3D%5Cfrac%7Bsin%28x%29%7D%7Bcos%28x%29%7D)
----> equation B
substitute equation B in equation A
solve for cos(x)
![cos^2(x)=\frac{1}{5}](https://tex.z-dn.net/?f=cos%5E2%28x%29%3D%5Cfrac%7B1%7D%7B5%7D)
square root both sides
![cos(x)=\pm\frac{1}{\sqrt{5}}](https://tex.z-dn.net/?f=cos%28x%29%3D%5Cpm%5Cfrac%7B1%7D%7B%5Csqrt%7B5%7D%7D)
but remember that the value of cos(x) is positive (IV quadrant)
![cos(x)=\frac{1}{\sqrt{5}}](https://tex.z-dn.net/?f=cos%28x%29%3D%5Cfrac%7B1%7D%7B%5Csqrt%7B5%7D%7D)
simplify
![cos(x)=\frac{\sqrt{5}}{5}](https://tex.z-dn.net/?f=cos%28x%29%3D%5Cfrac%7B%5Csqrt%7B5%7D%7D%7B5%7D)
36,000. you need to SUBTRACT to find "how many more"
They are always rational numbers
6×(1×5)=(6×1)×5
6×5=6×5
30=30
Always do the brackets first.
Follow BEDMAS
B = Brackets
E = Exponent
D = Division
M = multiplication
A = Addition
S = Substruction
Answer:
a) x⁵
b) y⁵x⁴
Step-by-step explanation:
a) there are 5 xs
b) 5 ys and 4 xs