Trigonometric graphs

$$\frac{2\pi}{3}$$  

$$\frac{4}{3}$$  

$$2\pi$$  

$$-\pi$$  

$$2\pi$$  

$$\pi$$  

$$4\pi$$  

$$3\pi$$  

$$\frac{\pi}{2}$$

$$\pi$$

$$2\pi$$

min = 5; max = 9

min = 2; max = 7

min = -5; max = 9

min = -9; max = -5

$$f\left(x\right)=5\sin\left(\frac{1}{2}x+3\right)+2$$  

$$f\left(x\right)=5\sin\left(2x+3\right)+2$$

$$f\left(x\right)=2\sin\left(\frac{1}{4}x+1\right)+5$$

$$f\left(x\right)=4\pi\sin\left(2x+1\right)-7$$

$$3\sin\left(2x-\frac{\pi}{3}\right)+9$$  

$$-3\sin\left(4x-\frac{\pi}{6}\right)-9$$  

$$f\left(x\right)=3\sin\left(4x-\frac{2\pi}{3}\right)-9$$  

$$-3\sin\left(4x+\frac{\pi}{6}\right)-9$$  

f(x)=3sin 2x - 1

f(x)=3sin 2x - 1

f(x)=2sin 3x + 1

f(x)=3sin 2x + 1

$$f\left(x\right)=-2\sin\left(x-\frac{\pi}{6}\right)$$  

$$f\left(x\right)=2\sin\left(x-\frac{\pi}{6}\right)$$  

$$f\left(x\right)=-2\sin\left(x+\frac{\pi}{6}\right)$$  

$$f\left(x\right)=2\sin\left(x+\frac{\pi}{6}\right)$$  

-1 downwards

$$\frac{\pi}{2}$$  to the left

$$\frac{\pi}{4}$$  to the left

$$\frac{\pi}{4}$$  to the right

$$\frac{\pi}{2}$$  to the right