Here's my problem:
Find an equation for a sinusoid that has a minimum at (30°,-1) and an adjacent maximum at (75°,7).
Please help! I've tried everything I can think of, but I'm really drawing a blank here, and I need my answer before 6:30 tonight!
So I'm pretty confident that the amplitude = 3, and the midpoint = 4, but I still need period and/or phase shift…
Best Answer
the half period of the $sin$ is the distance between consecutive local max and min. therefore half period $T/2 = 45^\circ = \pi/4 \to T = \pi/2.$ the sinusoidal is oscillating about the average value $\frac 12\left(7-(-1)\right) = 4$ and the amplitude is $7-4 = 3.$ putting all these together, we get $$y = 4 - 3\sin 4(t - \pi/24)=4-3\sin\left(4t - \frac{\pi}6\right).$$