# Ch 2  Acute Angles and Right Triangles

## Ch 2.1  Trigonometric Functions of Acute Angles

Cofunction Identities

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