introduction to the graphs of sine and cosine\nactivity 2\nlaunch:\nfill out the tables below:\nθ -2π -3π/2…
introduction to the graphs of sine and cosine\nactivity 2\nlaunch:\nfill out the tables below:\nθ -2π -3π/2 -π -π/2 0 π/2 π 3π/2 2π\n-sin θ\n \n \n \n \n0\n \n \n \n \nθ -2π -3π/2 -π -π/2 0 π/2 π 3π/2 2π\n-cos θ\n \n \n \n \n-1\n \n \n \n
Answer
Explanation:
Step1: Recall sine - function values
Use the property of the sine function (y = \sin\theta). We know that (\sin(-2\pi)=0), (\sin(-\frac{3\pi}{2}) = 1), (\sin(-\pi)=0), (\sin(-\frac{\pi}{2})=- 1), (\sin(0) = 0), (\sin(\frac{\pi}{2})=1), (\sin(\pi)=0), (\sin(\frac{3\pi}{2})=-1), (\sin(2\pi)=0). Then for (y =-\sin\theta), we just change the sign of these values.
Step2: Recall cosine - function values
Use the property of the cosine function (y=\cos\theta). We know that (\cos(-2\pi)=1), (\cos(-\frac{3\pi}{2}) = 0), (\cos(-\pi)=-1), (\cos(-\frac{\pi}{2})=0), (\cos(0) = 1), (\cos(\frac{\pi}{2})=0), (\cos(\pi)=-1), (\cos(\frac{3\pi}{2})=0), (\cos(2\pi)=1). Then for (y =-\cos\theta), we just change the sign of these values.
Answer:
| (\theta) | (-2\pi) | (-\frac{3\pi}{2}) | (-\pi) | (-\frac{\pi}{2}) | (0) | (\frac{\pi}{2}) | (\pi) | (\frac{3\pi}{2}) | (2\pi) |
|---|---|---|---|---|---|---|---|---|---|
| (-\sin\theta) | (0) | (- 1) | (0) | (1) | (0) | (-1) | (0) | (1) | (0) |
| (\theta) | (-2\pi) | (-\frac{3\pi}{2}) | (-\pi) | (-\frac{\pi}{2}) | (0) | (\frac{\pi}{2}) | (\pi) | (\frac{3\pi}{2}) | (2\pi) |
| (-\cos\theta) | (-1) | (0) | (1) | (0) | (-1) | (0) | (1) | (0) | (-1) |