How do you solve for t in 50 = 90sin(2pi*t / 26 + 3pi / 2) +115
50 = 90sin(2pi*t / 26 + 3pi / 2) +115
I am not allowed to solve this by drawing a graph. Hence, I have to show working.
I understand that I have to carry over the 115 and divide both sides by 90 which will get me
sin(2pi*t/26 + 3pi/2) = -13/18
For the next step, I think I am wrong as I did this
2pi*t/26 + 3pi/2 = 0.807
26(0.807 - 3pi/2) / 2pi
-16.16 + pi = -13
2pi - (-16.16) = 22.44
This is clearly wrong as the answers are 3.16 and 22.8 according to desmos. Is there a concept I am unaware of? Regardless, it would be best if you could show me the correct working anyway.