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June 12th, 2018, 11:07 PM  #1 
Newbie Joined: Jun 2018 From: State of Minas Gerais  Brasil Posts: 1 Thanks: 0  How to find the value at a certain angle of the sinusoid?
Good night sir, I have two sinusoidal functions whose sinusoidal maximum value is = 20 and the sinusoidal minimum = 20, we know that the maximum point the angle of the sinusoid = 90 ° or π / 2 in radians and corresponds to the value 20 I need to know an equation in which the second (red) signal switches will be valid, I know the angle is 150 ° and the corresponding value will be 10.30 (given by the software) but I want to know an equation for me to reach that value All I need to know, to be clearer is an equation where I will find the value in the blue sine when the red signal switches, I know that the angle at which it switches is 150 ° or 5π / 6 in radians. What is the equation for me to reach the value 10.30 that the red signal switches. Thanks to anyone who can help. 
June 18th, 2018, 04:49 AM  #2 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 
From your graph, it looks like your "sinusoid" has a minimum of 20, a maximum of +20, a period of 0.02, and f(0) = 0. From that information, $\displaystyle f(x)= 20\sin\left(\frac{2\pi}{0.02}x\right)$. If I understand this correctly, the "red signal switches" at the point where there is a vertical red line. That line has $\displaystyle y= f(x)= 20\sin\left(\frac{2\pi}{0.02}x\right)= 10.03$. Solving that, we have $\displaystyle \sin\left(\frac{2\pi}{0.02}x\right)= 0.5015$, so that $\displaystyle \frac{2\pi}{0.02}x= 0.5253$. $\displaystyle x= \frac{0.5253(0.02)}{2\pi}= \frac{0.0105}{6.283}= 0.00167$.
Last edited by skipjack; June 18th, 2018 at 08:16 AM. 

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