Graphing Sine and Cosine Review Graphing Sine and Cosine Graph the following functions. State the amplitude, period, phase shift, vertical shift and reflection. 𝑦=2𝑐𝑜𝑠 𝑥− 3𝜋 2 −1 𝑦=−3𝑠𝑖𝑛 𝑥+ 5𝜋 6 +4

Finding an Equation for a Sine/Cosine Graph Steps: Find the midline (horizontal middle) of the graph. This is your “d” value. Calculate the distance from the midline to the top (or bottom) of your graph. This is your “a” value. Highlight one complete wave of your graph. Calculate the distance of the one wave. This is your period. Use the period formula, 2𝜋 𝑏 and the distance calculated to find your “b” value. Identify the starting point of your highlight wave. This is your phase shift. Use your phase shift formula, 𝑐 𝑏 , and the “b” value found in step 3 to find your “c” value. Place you’re a, b, c, and d values into the general form to obtain the final equation: f x =a sin (𝑏𝑥−𝑐) +𝑑 **Answer may vary

Review Extension Write the Equation that corresponds to each graph.

Graphing Other Trigonometric Functions Keeper 14 Accelerated Pre-Calculus

Properties Tangent Properties of the Tangent Function

Period of Tangent For 𝑦=atan 𝑏𝑥+𝑐 , 𝑤ℎ𝑒𝑟𝑒 𝑏≠0, 𝑝𝑒𝑟𝑖𝑜𝑑= 𝜋 𝑏 .

Asymptotes of Tangent To find the vertical asymptotes of any tangent function of the form 𝑦= atan 𝑏𝑥+𝑐 +𝑑, solve: 𝑏𝑥+𝑐=− 𝜋 2 𝑎𝑛𝑑 𝑏𝑥+𝑐= 𝜋 2

Examples Locate the asymptote and graph the function 𝑦=−2 tan 𝑥 2 +3

Graphing Secant and Cosecant Keeper 14 Accelerated Pre-Calculus

Steps for Graphing Secant and Cosecant Graph the corresponding cosine (for secant) or sine (for cosecant) wave. Identify the midline of the graph. Draw asymptotes through the points that cross the midline (3 asymptotes total). Draw U’s between the asymptotes (at least 2 U’s, one up and one down).

Properties of the Cotangent Function For 𝑦=a𝑐𝑜𝑡 𝑏𝑥+𝑐 , 𝑤ℎ𝑒𝑟𝑒 𝑏≠0, 𝑝𝑒𝑟𝑖𝑜𝑑= 𝜋 𝑏 . To find the vertical asymptotes of any tangent function of the form 𝑦= a𝑐𝑜𝑡 𝑏𝑥+𝑐 +𝑑, solve: 𝑏𝑥+𝑐=−𝜋 𝑎𝑛𝑑 𝑏𝑥+𝑐=𝜋

Examples Locate the asymptote and graph the function 𝑦= cot 𝑥 3 𝑦=3𝑐𝑜𝑡 𝑥 2

Properties of Cosecant and Secant Functions

Examples Sketch Graphs of Cosecant and Secant Functions 𝑦=csc⁡ 𝑥+ 𝜋 2