Chapter 2 Trigonometry

Ch 2  Acute Angles and Right Triangles


Ch 2.1  Trigonometric Functions of Acute Angles

Cofunction Identities–4_Q&

Finding sin (30º),cos (30º), tan (30º), sin (60º),cos (60º), tan (60º), sin (45º),cos (45º), tan (45º)

Using the Ratio of the Sides of 30–60–90 Triangle or 45-45-90 Triangle to solve the Triangles

Examples: Solve a 30–60–90 Right Triangle

Examples: Solve a 45–45–90  Right Triangle

Ch 2.2  Trigonometric Functions of Non-Acute Angles

Examples: Determine the Reference Angle for a Given Angle :

Determining the reference angle θ=221º;

Determining the reference angle θ=347º;

Determining the reference angle θ= –125º

Determining the reference angles for cos 210º, tan (–45)º;

Determining the Reference Angle for θ=460º, θ=165º, θ= –40º, θ= –283º

Determining Reference Angles of 120º, 210º, –45º, 270º

Determining Trigonometric Function of cos (60º), tan (180º), csc (225º), sec (–240º), cot (540º) from a Unit Circle

Determining Trigonometric Function Values of 90º, 150º, –60º, from a unit Circle

Determining Trigonometric Function Values of –990º from a unit Circle

Ch 2.3  Finding Trigonometric Function Values Using a Calculator

Determining Trigonometric Function Values on the Calculator :
sin (30º), cos (45º), tan (–264º), sec (102.5º), csc (432º), cot (–23.45º)

Using Inverse Trigonometric functions to Find Angles :

Solving for θ for sin θ=0.7523, tan θ=3.54, and Find the Sides and Angles of a Right Triangle

Solving for θ for cos-1(1/2 ) and tan-1(–1)

Finding the Trigonometric Function Values Using Calculator: cos (369.18°), tan (426.62°), sin (46.6°), cot (17.9°)
Solving for θ for csc θ=3.6, cot θ=2.1, csc θ=1.63, sec θ=7.25

Ch 2.4  Solving Right Triangles

Example: Determining the Measure of an Angle of a Right Triangle Using a Trig Equation

Solving the sides and angles of Right Triangles

Applications : Angle of Elevation

Finding the Height of an Object

Finding the Height of a Tree

Finding the Height of a Flagpole (Part 1 of the video)

Simple Distance Problem – A Hiking Problem

Determining the Speed of a Boat

Ch 2.5  Further Applications of Right Triangles

Applications : Finding the Distance of a Ship on an Angle of Bearing (Part 2 of the video)

Finding the Height of a Building

Finding the Length of x Using Right Triangle Trigonometry