The Other Trigonometric Functions

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GRAPHS OF OTHER TRIG FUNCTIONS

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Presentation transcript:

The Other Trigonometric Functions Section 7-5 The Other Trigonometric Functions

Six Trig. Functions sine (sin θ) cosecant (csc θ) cosine (cos θ) secant (sec θ) tangent (tan θ) cotangent (cot θ)

Trig Formulas sin θ = csc θ = cos θ = sec θ = tan θ = cot θ =

Formulas in terms of sin and cos tan θ = sec θ = cot θ = csc θ =

Positive Quadrants

Using a Calculator Because we do not have secant, cosecant, and cotangent buttons on the calculator, we need to use the formulas of these functions that are given in terms of sine, cosine, and tangent.

Using a Calculator Example 1: Use a calculator to find sec 22º.

Using a Calculator Example 2: Use the calculator to find cot 185º.

Using a Calculator Example 3: Use a calculator to find csc 3.

Given a quadrant and one of the trig functions of θ we can use the formulas and the circle formula to find the other five trig functions.

Finding Trig. Functions Example 4: Find the value of the other five trig. functions if tan θ = and π < θ < 2π. *First, determine which quadrant the angle is in.*

Finding Trig. Functions (continued) The angle must be in the third quadrant. And we know tan θ =

HOMEWORK (Day 1) pg. 285; (class exercises) 5 – 7 all pg. 285; (written exercises) 1, 2

pg. 285 5) III IV a. cos θ = -3/5 b. tan θ = -4/3 c. cot θ = -3/4 d. sec θ = -5/3 e. csc θ = 5/4 1) a. -5.671 b. -0.1051 c. -1.043 d. -1.855 2) a. 1.019 b. -1.252 c. -0.1425 d. 0.6466

Example 5: Find the exact value of each expression or state that the value is undefined. sin 120° = csc 120° = cos 120° = sec 120° = tan 120° = cot 120° =

Example 6: Find the exact value of each expression or state that the value is undefined. csc 90° = 1 sec 90° = undefined tan 90° cot 90° = 0

Graphing y = tan θ Use a calculator to fill in the chart. If you get an error for an answer, write “undefined” in the box. tan 0° = tan 45° = tan -45° = tan 90° = tan -90° = tan 180° = tan -180° = tan 270° = tan -270° = tan 360° = tan -360° =

Graphing y = tan θ Draw the x and y axes Draw the asymptotes at the undefined values Plot the points where tangent is defined

Graph of y = tan θ

HOMEWORK (Day 2) pg. 285; 9 pg. 286; 13, 15, 24 – 28 even