10. Writing the equation of trig functions

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

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

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

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

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

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

Examples Write the equation for sin

Example Write the equation for cos

Example Write the equation for sin and for cos

Write the equation for sin and cos