Answer:
In the first quadrant are solutions of the form ![x=\dfrac{\pi}{6}+2\pi k,\ k\in Z.](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B%5Cpi%7D%7B6%7D%2B2%5Cpi%20k%2C%5C%20k%5Cin%20Z.)
In the second quadrant are solutions of the form ![x=\dfrac{5\pi}{6}+2\pi k,\ k\in Z.](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B5%5Cpi%7D%7B6%7D%2B2%5Cpi%20k%2C%5C%20k%5Cin%20Z.)
Step-by-step explanation:
First, solve the equation
This equation is equivalent to equation
![\tan^2 x=\dfrac{1}{3},\\ \\\tan x=\dfrac{1}{\sqrt{3} }\ \text{or }\tan x=-\dfrac{1}{\sqrt{3} }.](https://tex.z-dn.net/?f=%5Ctan%5E2%20x%3D%5Cdfrac%7B1%7D%7B3%7D%2C%5C%5C%20%5C%5C%5Ctan%20x%3D%5Cdfrac%7B1%7D%7B%5Csqrt%7B3%7D%20%7D%5C%20%5Ctext%7Bor%20%7D%5Ctan%20x%3D-%5Cdfrac%7B1%7D%7B%5Csqrt%7B3%7D%20%7D.)
The equation
has the solution
![x=\arctan \dfrac{1}{\sqrt{3} }+\pi k,\ k\in Z,\\ \\x=\dfrac{\pi}{6}+\pi k,\ k\in Z.](https://tex.z-dn.net/?f=x%3D%5Carctan%20%5Cdfrac%7B1%7D%7B%5Csqrt%7B3%7D%20%7D%2B%5Cpi%20k%2C%5C%20k%5Cin%20Z%2C%5C%5C%20%5C%5Cx%3D%5Cdfrac%7B%5Cpi%7D%7B6%7D%2B%5Cpi%20k%2C%5C%20k%5Cin%20Z.)
The equation
has the solution
![x=\arctan \left(-\dfrac{1}{\sqrt{3} }\right)+\pi k,\ k\in Z,\\ \\x=-\dfrac{\pi}{6}+\pi k,\ k\in Z.](https://tex.z-dn.net/?f=x%3D%5Carctan%20%5Cleft%28-%5Cdfrac%7B1%7D%7B%5Csqrt%7B3%7D%20%7D%5Cright%29%2B%5Cpi%20k%2C%5C%20k%5Cin%20Z%2C%5C%5C%20%5C%5Cx%3D-%5Cdfrac%7B%5Cpi%7D%7B6%7D%2B%5Cpi%20k%2C%5C%20k%5Cin%20Z.)
In the first quadrant are solutions of the form ![x=\dfrac{\pi}{6}+2\pi k,\ k\in Z.](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B%5Cpi%7D%7B6%7D%2B2%5Cpi%20k%2C%5C%20k%5Cin%20Z.)
In the second quadrant are solutions of the form ![x=\dfrac{5\pi}{6}+2\pi k,\ k\in Z.](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B5%5Cpi%7D%7B6%7D%2B2%5Cpi%20k%2C%5C%20k%5Cin%20Z.)
Answer:
24) x = 9.2
25) x = 30.8
Step-by-step explanation:
Given
See attachment for triangles
Solving (24)
To solve for x, we make use of cosine formula
i.e.
cos(40) = adjacent ÷ hypotenuse
So, we have:
cos(40) = x ÷ 12
Multiply both sides by 12
12 cos(40) = x
12 * 0.7660 = x
x = 9.2
Solving (25)
To solve for x, we make use of sine formula
i.e.
sin(25) = opposite ÷ hypotenuse
So, we have:
sin(25) = 13 ÷ x
Multiply both sides by
x sin(25) = 13
Divide by sin(25)
x = 13 ÷ sin(25)
Using a calculator
x = 30.8
Answer:
D
Step-by-step explanation: