Answer:
that is so much work um. i believe you have to graph first and look at the given problems
Answer:
The solutions are 0° and 3π
Step-by-step explanation:
On solving the equation given;
![sin(\frac{3\pi}{2}+x )+ sin(\frac{3\pi}{2}+x ) = -2\\2sin(\frac{3\pi}{2}+x ) = -2\\sin(\frac{3\pi}{2}+x ) = -1\\\frac{3\pi}{2}+x = sin^{-1}-1\\ \frac{3\pi}{2}+x = -\frac{\pi}{2} \\x = -\frac{\pi}{2} -\frac{3\pi}{2} \\x = \frac{-4\pi}{2} \\x = -2\pi\\](https://tex.z-dn.net/?f=sin%28%5Cfrac%7B3%5Cpi%7D%7B2%7D%2Bx%20%29%2B%20sin%28%5Cfrac%7B3%5Cpi%7D%7B2%7D%2Bx%20%29%20%3D%20-2%5C%5C2sin%28%5Cfrac%7B3%5Cpi%7D%7B2%7D%2Bx%20%29%20%3D%20-2%5C%5Csin%28%5Cfrac%7B3%5Cpi%7D%7B2%7D%2Bx%20%29%20%3D%20-1%5C%5C%5Cfrac%7B3%5Cpi%7D%7B2%7D%2Bx%20%20%3D%20sin%5E%7B-1%7D-1%5C%5C%20%5Cfrac%7B3%5Cpi%7D%7B2%7D%2Bx%20%3D%20-%5Cfrac%7B%5Cpi%7D%7B2%7D%20%5C%5Cx%20%3D%20-%5Cfrac%7B%5Cpi%7D%7B2%7D%20-%5Cfrac%7B3%5Cpi%7D%7B2%7D%20%5C%5Cx%20%3D%20%20%5Cfrac%7B-4%5Cpi%7D%7B2%7D%20%5C%5Cx%20%3D%20-2%5Cpi%5C%5C)
<u>Since sin is negative in the 3rd and 4th quadrant, </u>
In the 3rd quadrant;
x =180°+2π
x = π + 2π
x = 3π
In the 4th quadrant;
x = 360°-2π
x = 2π-2π
x = 0°
Answer:
3x
Step-by-step explanation:
The result of the given exponential expression is given as 1/8, 3^2, 1/5 and 5^-2
<h3>Properties of exponents</h3>
Some of the properties of exponents are expressed as shown below;
1) a^-n = 1/a^n
In order to answer the given questions, we will use the following properties above;
3^-4 = 1/3^4 where a is equivalent to 3 and n is equivalent to 4
Similarly;
1/2^3 = 2^-3 = 1/8
For the expression 1/3^-2
1/3^-2 = 1/(1/3^2)
1/3^-2 = 3^2
For the expression 5^-1
5^-1 = 1/5^1
5^-1 = 1/5
Also for 1/5^2
1/5^2 = 1/25 = 5^-2
Hence the result of the given exponential expression is given as 1/8, 3^2, 1/5 and 5^-2
Learn more on exponent here: brainly.com/question/11975096
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