Warm Up The terminal side passes through (1, -2), find cosƟ and sinƟ. The sine of an angle is − 𝟓 𝟏𝟑 . The angle is in Quadrant IV. What is the cosine of the angle? Find the reference angles for 𝟑𝟖𝝅 𝟐𝟏 and − 𝟏𝟖𝝅 𝟏𝟑 Solve in radians: cosƟ = 0 Find the exact value of 𝒍𝒐𝒈 𝟒 𝒔𝒊𝒏𝟏𝟓𝟎° − 𝟐 𝟓 𝟓 𝟓 𝟓 𝟏𝟐 𝟏𝟑 𝟒𝝅 𝟐𝟏 , 𝟓𝝅 𝟏𝟑 𝝅 𝟐 ±𝒏𝝅 − 𝟏 𝟐

Graphing Sine and Cosine Functions Complete classwork problems A – D You should have a table, 2 complete graphs (on the same grid), and key points in degrees and radians for each graph.

Use the unit circle to complete the table for each function. Graph y=sin x. Use a scale of 𝜋 12 radians on the x-axis and 0.1 on the y-axis. D. For each graph, find the following in radians and degrees: period zeroes y-intercept amplitude domain range x 𝜋 6 𝜋 4 𝜋 3 𝜋 2 2𝜋 3 3𝜋 4 5𝜋 6 𝜋 7𝜋 6 5𝜋 4 4𝜋 3 3𝜋 2 5𝜋 3 7𝜋 4 11𝜋 6 2𝜋 y=sin x   y=cosx

Graph Sine & Cosine 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 𝟐𝝅 -0.1 𝝅 𝟏𝟐 𝝅 -0.2 -0.3 -0.4 -0.5 -0.6 -0.7 -0.8 -0.9 -1.0

𝒚=𝒔𝒊𝒏𝒙 Period: 2𝜋, 360 Amplitude: 1 Domain: −∞<𝑥<∞ Range: −1≤𝑦≤1 1.0 Period: 2𝜋, 360 Amplitude: 1 Domain: −∞<𝑥<∞ Range: −1≤𝑦≤1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 𝝅 𝟏𝟐 𝝅 𝟔 𝝅 𝟒 𝝅 𝟑 𝟓𝝅 𝟏𝟐 -0.1 𝝅 𝟐 𝟕𝝅 𝟏𝟐 𝟐𝝅 𝟑 𝟑𝝅 𝟒 𝟓𝝅 𝟔 𝟏𝟏𝝅 𝟏𝟐 𝝅 𝟏𝟑𝝅 𝟏𝟐 𝟕𝝅 𝟔 𝟓𝝅 𝟒 𝟒𝝅 𝟑 𝟏𝟕𝝅 𝟏𝟐 𝟑𝝅 𝟐 𝟏𝟗𝝅 𝟏𝟐 𝟓𝝅 𝟑 𝟕𝝅 𝟒 𝟏𝟏𝝅 𝟔 𝟐𝟑𝝅 𝟏𝟐 𝟐𝝅 -0.2 -0.3 -0.4 -0.5 Zeroes: 0,𝜋,2𝜋 0ᵒ,180ᵒ,360 ̊ y-intercept: (0,0) -0.6 -0.7 -0.8 -0.9 -1.0

𝒚=𝒄𝒐𝒔𝒙 Zeroes: 𝜋 2 , 3𝜋 2 90ᵒ, 270 ̊ y-intercept: (0,1) 1.0 0.9 0.8 Zeroes: 𝜋 2 , 3𝜋 2 90ᵒ, 270 ̊ y-intercept: (0,1) 0.7 0.6 0.5 0.4 0.3 0.2 0.1 𝝅 𝟏𝟐 𝝅 𝟔 𝝅 𝟒 𝝅 𝟑 𝟓𝝅 𝟏𝟐 -0.1 𝝅 𝟐 𝟕𝝅 𝟏𝟐 𝟐𝝅 𝟑 𝟑𝝅 𝟒 𝟓𝝅 𝟔 𝟏𝟏𝝅 𝟏𝟐 𝝅 𝟏𝟑𝝅 𝟏𝟐 𝟕𝝅 𝟔 𝟓𝝅 𝟒 𝟒𝝅 𝟑 𝟏𝟕𝝅 𝟏𝟐 𝟑𝝅 𝟐 𝟏𝟗𝝅 𝟏𝟐 𝟓𝝅 𝟑 𝟕𝝅 𝟒 𝟏𝟏𝝅 𝟔 𝟐𝟑𝝅 𝟏𝟐 𝟐𝝅 -0.2 -0.3 Period: 2𝜋, 360 ̊ Amplitude: 1 Domain: −∞<𝑥<∞ Range: −1≤𝑦≤1 -0.4 -0.5 -0.6 -0.7 -0.8 -0.9 -1.0

Section 7-5 The Other Trigonometric Functions Objective: To find the values of the tangent, cotangent, secant, and cosecant functions and to sketch the functions’ graphs.

We can define other trig functions in terms of (x,y) and r. 𝑐𝑜𝑠𝜃= 𝑥 𝑟 𝑠𝑖𝑛𝜃= 𝑦 𝑟 We can define other trig functions in terms of (x,y) and r. Name Abbreviation Definition tangent of  tan  cotangent of  cot  secant of  sec  cosecant of  csc 

What is sin ÷ cos? tan What is cos ÷ sin? cot 𝑦 𝑟 ÷ 𝑥 𝑟 = 𝑦 𝑟 ∗ 𝑟 𝑥 = 𝑦 𝑥 = tan What is cos ÷ sin? 𝑥 𝑟 ÷ 𝑦 𝑟 = 𝑥 𝑟 ∗ 𝑟 𝑦 = 𝑥 𝑦 = cot

Reciprocals tan & cot are reciprocals cos & sec are reciprocals sin & csc are reciprocals

Find the value of each expression to four significant digits. A.) tan 203° B.) cot 165° C.) csc (-1) D.) sec 11 Hint:

Find the value of each expression to four significant digits.

Graph 𝑦= tan 𝜃 −3𝜋≤𝜃≤3𝜋 Window xmin: −3𝜋 xmax: Table Setup xscl: ymin: ymax: yscl: xres: −3𝜋 Table Setup TblStart: 0 ∆Tbl: 𝜋 4 Indpnt: Auto Depend: Auto: 3𝜋 𝜋 4 −10 10 1 1

Graph 𝑦= tan 𝜃 −3𝜋≤𝜃≤3𝜋 Domain Range Period Asymptotes

Graph 𝑦= sec 𝜃 −3𝜋≤𝜃≤3𝜋 Domain Range Period Asymptotes

Graph 𝑦= sec 𝜃 −3𝜋≤𝜃≤3𝜋 Why can’t 𝑠𝑒𝑐𝜃 be between -1 and 1?

Homework Finish All Graphs