Answer: [tex]\frac{23\pi} {12}[/tex], [tex]\frac{-25\pi} {12}[/tex]
Step-by-step explanation:
2π = [tex]\frac{24\pi} {12}[/tex]
positive: [tex]\frac{-\pi} {12} + \frac{24\pi} {12}[/tex] = [tex]\frac{23\pi} {12}[/tex]
negative: [tex]\frac{-\pi} {12} - \frac{24\pi} {12}[/tex] = [tex]\frac{-25\pi} {12}[/tex]
*********************************************************************************
Answer: A
Step-by-step explanation:
Quadrant I: 0 - [tex]\frac{\pi} {2}[/tex]
= 0 - [tex]\frac{2\pi} {4}[/tex]
Quadrant II: [tex]\frac{\pi} {2}[/tex] - [tex]{\pi}[/tex]
= [tex]\frac{2\pi} {4}[/tex] - [tex]\frac{4\pi} {4}[/tex]
Quadrant III: [tex]{\pi}[/tex] - [tex]\frac{3\pi} {2}[/tex]
= [tex]\frac{4\pi} {4}[/tex] - [tex]\frac{6\pi} {4}[/tex]
Quadrant IV: [tex]\frac{3\pi} {2}[/tex] - [tex]2\pi[/tex]
= [tex]\frac{6\pi} {4}[/tex] - [tex]\frac{8\pi} {4}[/tex]
[tex]\frac{9\pi} {4}[/tex] - [tex]\frac{8\pi} {4}[/tex] = [tex]\frac{\pi} {4}[/tex] which is in Quadrant I after 1 rotation.
*********************************************************************************
Answer: 118.96 ft
Step-by-step explanation:
[tex]\frac{180}{\pi} = \frac{20}{\theta}[/tex]
180(θ) = 20π
θ = [tex]\frac{20\pi} {180}[/tex]
θ = [tex]\frac{\pi} {9}[/tex]
A = [tex]\frac{1}{2}[/tex]r²θ
2470 = [tex]\frac{1}{2}[/tex]r²[tex](\frac{\pi} {9})[/tex]
[tex]\frac{2470(2)(9)}{\pi}[/tex] = r²
14,152 = r²
118.96 = r
*********************************************************************************
Answer: [tex]\frac{13\pi}{36}[/tex]
Step-by-step explanation:
[tex]\frac{\pi }{180} = \frac{\theta}{65}[/tex]
[tex]\frac{65\pi}{180}[/tex] = θ
[tex]\frac{13\pi}{36}[/tex] = θ
