I'm not sure how to solve this equation algebraically:
38=20sin((2pi(t))/36)+22
I know the answer should be about 5.3 since I graphed it.
I can get as far as removing 22 from the right and then removing 20 from the right by dividing by 20. To get 0.8=sin((2pi(t))/36)
PI*t/18=arcsin.8
t=18/PI * arcsin(.8)
Your calculator is needed on that.
thanks!
To solve the equation algebraically, you are on the right track by getting it in the form `sin((2πt)/36) = 0.8`. Now, let's break down the steps further:
Step 1: Subtract 22 from both sides of the equation:
38 - 22 = 20sin((2πt)/36) + 22 - 22
16 = 20sin((2πt)/36)
Step 2: Divide both sides of the equation by 20:
16/20 = (20sin((2πt)/36))/20
0.8 = sin((2πt)/36)
Now you have the equation `sin((2πt)/36) = 0.8`. To find the value of t that satisfies this equation, you need to take the inverse sin (also known as arcsin or sin^(-1)) of 0.8.
The inverse sin function will give you the angle whose sine is 0.8. You can use either a calculator's inverse sin function (often denoted as sin^(-1) or arcsin) or consult a table of trigonometric values.
Using a calculator, perform the inverse sin operation on 0.8:
t = (2π/36) * sin^(-1)(0.8)
t ≈ 2.094
Therefore, the value of t that satisfies the equation is approximately 2.094, which is relatively close to the 5.3 value you obtained from graphing the equation.