# Finding the Equations of Trigonometric Functions - Radians (Part 1)

1. 1
Find the equation of the sin function given:

Amplitude = 5
Period =$\pi$
Phase shift = $\frac{\pi}{6}$ to the right.
Vertical Shift = 4 units up.
2. 2
Find the equation of the cos function given:

Amplitude = 4 (reflected over the x-axis)
Period =$\frac{\pi}{3}$
Phase shift =$\frac{\pi}{6}$ to the left.
Vertical Shift = 5 units down.
3. 3
Find the equation of the sin function given:

Amplitude = 7
Period =$\frac{\pi}{2}$
Phase shift = $\frac{\pi}{4}$ to the right.
Vertical Shift = 10 units down.
4. 4
Find the equation of the sin function given:

Amplitude = 5
Period =$\frac{2\pi}{3}$
Phase shift = $\frac{7\pi}{6}$ to the right.
Vertical Shift = 75 units down.
5. 5
Find the equation of the cos function given:

Amplitude = 7 (reflected over the x-axis)
Period =$\frac{\pi}{4}$
Phase shift = $\frac{11\pi}{6}$ to the left.
Vertical Shift = 93 units down.
6. 6
Find the equation of the cos function given:

Amplitude = 9 (reflected in the x-axis)
Period =4
Phase shift = $\frac{5\pi}{4}$ to the left.
Vertical Shift = 11 units down.
7. 7
Find the equation of the sin function given:

Amplitude = 15
Period =3
Phase shift = $\frac{5\pi}{3}$ to the right.
Vertical Shift = 23 units up.
8. 8
Find the equation of the cos function given:

Amplitude = 34 (reflected in the x-axis)
Period =$3\pi$
Phase shift = $\frac{5\pi}{4}$ to the left.
Vertical Shift = 49 units up.
9. 9
Find the equation of the sin function given:

Amplitude = $\alpha$ (reflected in the x-axis)
Period =$\phi$
Phase shift = $\triangle$ to the right.
Vertical Shift = $\heartsuit$ units up.
10. 10
Find the equation of the cos function given:

Amplitude = "a" (reflected in the x-axis)
$$e=mc^2$$