Sec 6.2 Trigonometry of Right Triangles Objectives: To define and use the six trigonometric functions as ratios of sides of right triangles. To review.

Slides:



Advertisements
Similar presentations
D. Trigonometry Math 10: Foundations and Pre-Calculus FP10.4 Develop and apply the primary trigonometric ratios (sine, cosine, tangent) to solve problems.
Advertisements

4.1 – Right Triangle Trigonometry. Sin Ɵ = opp hyp.
Section Review right triangle trigonometry from Geometry and expand it to all the trigonometric functions Begin learning some of the Trigonometric.
Day 2 and Day 3 notes. 1.4 Definition of the Trigonometric Functions OBJ:  Evaluate trigonometric expressions involving quadrantal angles OBJ:  Find.
Trigonometry/Precalculus ( R )
Chapter 14 Day 5 Trig Functions of Any Angle.  We can also evaluate trig functions of an angle that contains a point that isn’t necessarily on the unit.
Drill Find the missing side length of right triangle ABC. Assume side C is the hypotenuse. 1.A = 7, B = 3 2.A = 9, C = 15.
4.4 Trigonometric Functions of any Angle Objective: Students will know how to evaluate trigonometric functions of any angle, and use reference angles to.
1 7.3 Evaluating Trig Functions of Acute Angles In this section, we will study the following topics: Evaluating trig functions of acute angles using right.
8.3 Solving Right Triangles
4.2 Trigonometric Function: The Unit circle. The Unit Circle A circle with radius of 1 Equation x 2 + y 2 = 1.
5.1 Trigonometric Functions of Acute Angles Fri Oct 17 Do Now Solve for x 1) 1^2 + x^2 = 2^2 2) x^2 + x^2 = 1.
Sec 6.2 Trigonometry of Right Triangles
Right Triangle Trigonometry
4.3 Right Triangle Trigonometry Pg. 484 # 6-16 (even), (even), (even) –Use right triangles to evaluate trigonometric functions –Find function.
Right Triangle Trigonometry
Right Triangle Trigonometry
Chapter 4 Trigonometric Functions Right Triangle Trigonometry Objectives:  Evaluate trigonometric functions of acute angles.  Use fundamental.
4.3 Right Triangle Trigonometry
6.2: Right angle trigonometry
Right Triangle Trigonometry
Bell Work Find all coterminal angles with 125° Find a positive and a negative coterminal angle with 315°. Give the reference angle for 212°.
TRIGONOMETRIC RATIOS AND THE UNIT CIRCLE Mrs. White Precalculus 5.2/5.4.
13.2 – Define General Angles and Use Radian Measure.
TOP 10 Missed Mid-Unit Quiz Questions. Use the given function values and trigonometric identities to find the indicated trig functions. Cot and Cos 1.Csc.
Math III Accelerated Chapter 13 Trigonometric Ratios and Functions 1.
2.1 Six Trig Functions for Right Triangles
Tuesday 3/24. Warm Up Determine the six trigonometric ratios for the following triangle: y r x θ sin θ =csc θ = cos θ =sec θ = tan θ =cot θ = What if.
Class Work 1.Sketch a right triangle that has acute angle , and find the five other trig ratios of . 2.Evaluate the expression without using a calculator.
Do Now: Graph the equation: X 2 + y 2 = 1 Draw and label the special right triangles What happens when the hypotenuse of each triangle equals 1?
Right Triangle Trigonometry
Chapter 14 Day 5 Trig Functions of Any Angle.  The of a circle is a portion of the of a circle. arc circumference.
4.3 Right Triangle Trigonometry
13.1 – Use Trig with Right Triangles
1 What you will learn  How to find the value of trigonometric ratios for acute angles of right triangles  More vocabulary than you can possibly stand!
Trig/Precalculus Section 5.1 – 5.8 Pre-Test. For an angle in standard position, determine a coterminal angle that is between 0 o and 360 o. State the.
Conversion of Radians and Degrees Degree Radian Radians Degrees Example 1Converting from Degrees to Radians [A] 60° [B] 30° Example 2Converting from Radians.
Section 1.4 Trigonometric Functions an ANY Angle Evaluate trig functions of any angle Use reference angles to evaluate trig functions.
Section 5.2 Right Triangle Trigonometry. Function Values for Some Special Angles.
Pg. 362 Homework Pg. 362#56 – 60 Pg. 335#29 – 44, 49, 50 Memorize all identities and angles, etc!! #40
4.3 Trigonometry Extended: The Circular Functions
Right Triangle Trigonometry
Knight’s Charge: Precalculus 41 Right Triangle Trigonometry 1.
Trigonometry Ratios.
Quiz 36 Application Problem #1 1. Convert from revolutions into radians 2. Write the Equation and fill in information 3. Convert from ft/sec to mi/hr 4.
4.2 Trig Functions of Acute Angles. Trig Functions Adjacent Opposite Hypotenuse A B C Sine (θ) = sin = Cosine (θ ) = cos = Tangent (θ) = tan = Cosecant.
Lesson 46 Finding trigonometric functions and their reciprocals.
Trigonometry Section 4.2 Trigonometric Functions: The Unit Circle.
6.1 – 6.5 Review!! Graph the following. State the important information. y = -3csc (2x) y = -cos (x + π/2) Solve for the following: sin x = 0.32 on [0,
4.3 Right Triangle Trigonometry Objective: In this lesson you will learn how to evaluate trigonometric functions of acute angles and how to use the fundamental.
Algebra 2 cc Section 7.1 Solve right triangles “Trigonometry” means triangle measurement and is used to solve problems involving triangle. The sides of.
Trig Functions – Part Pythagorean Theorem & Basic Trig Functions Reciprocal Identities & Special Values Practice Problems.
13.1 Right Triangle Trigonometry ©2002 by R. Villar All Rights Reserved.
13.1 Right Triangle Trigonometry. Definition  A right triangle with acute angle θ, has three sides referenced by angle θ. These sides are opposite θ,
5.2 Trigonometric Ratios in Right Triangles. A triangle in which one angle is a right angle is called a right triangle. The side opposite the right angle.
Trigonometry Identities.
Trigonometric Function: The Unit circle
Right Triangle Trigonometry (Section 4-3)
Trigonometric Functions of Acute Angles
Warm – Up: 2/4 Convert from radians to degrees.
Trigonometric Functions
Unit 7B Review.
Warm-up: Find the tan 5
Warm-up: Find the exact values of the other 5 trigonometric functions given sin= 3 2 with 0 <  < 90 CW: Right Triangle Trig.
Right Triangle Ratios Chapter 6.
2) Find one positive and one negative coterminal angle to
Trig. Ratios in a Coordinate System
Sec 6.2 Trigonometry of Right Triangles
Academy Algebra II THE UNIT CIRCLE.
5-3 The Unit Circle.
Presentation transcript:

Sec 6.2 Trigonometry of Right Triangles Objectives: To define and use the six trigonometric functions as ratios of sides of right triangles. To review special right triangles. To solve right triangles using trigonometric ratios.

Trigonometric Ratios

Ex 1. Find the six trig ratios of the angle .

Ex 2. Sketch a right triangle with acute angle  and find the other five trig ratios of . a)b)

Class Work 1.Find the six trig ratios of the angle . 2.a) Find sin  and cos  b) Find tan  and cot  c) Find sec  and csc  7 6    7 4

3. Sketch a right triangle with acute angle  and find the other five trig ratios of . a) b)

Special Triangles  30  60  1 2  in degrees  in radians sin  cos  tan  csc  sec  cot  30  45  60 

Ex 3. Evaluate the following without a calculator. a)b)

Ex 4. Find the exact value of x. a)b) x  60  x 21

Class Work Evaluate the expression without using a calculator. 4. sin 30  csc 30  5.

Find the exact value of x. 6.7.

Solving a Right Triangle A triangle has six parts—three angles and three sides. To solve a triangle means to determine all of its parts from the information known about the triangle. – In other words, we determine the lengths of the three sides and the measures of the three angles.

Ex 5. Solve the triangle. a)b)

Class Work Solve the triangle. 8.9.

10. From the top of a 200 ft lighthouse, the angle of depression to a ship in the ocean is 23 . How far is the ship from the base of the lighthouse?

HW #2 p odd, 49, 50.