1. 10. Writing the equation of trig functions

2. Sin, Cos, Csc, and Sec A sin B(θ-HS)+VS
A, HS, VS, and Per will be given to you (HS will sometimes be called Phase shift)
To find B, set the period equal to 2π/B
Write the equation as above, then distribute the B

3. Examples A = 4, Per = π/3, PS = π/4, VS = -3 for sin
A = -6, Per = 2π, PS = -5π/2, VS = 2 for cos
A = -1/2, Per = π/6, PS = π/6, VS = 1 for csc
A = 5/8, Per = 2π/3, PS = 2π, VS = -4 for sec

4. Tan, Cot
Everything is the same, except to find B, set period = π/B

5. Examples A = 2, Per = π/3, PS = π/4, VS = -3 for tan
A = -5, Per = π/2, PS = -π/2, VS = 1 for cot

6. Writing the equation from a graph
You must find A, Per, HS, VS from the graph
Then do what we just did
We will only look at sin/cos graphs

7. Steps You will be given a graph with more than one period
Highlight one period of a sin graph or one period of a cos graph depending on what the question is asking for
Mark the vertical middle of your highlighted section
A = top y value – middle y value
VS = middle y value
Per = right x value – left x value
HS = left x value

8. Examples
Write the equation for sin

9. Example
Write the equation for cos

10. Example
Write the equation for sin and for cos

11. Write the equation for sin and cos