 S INE (S IN ): Opposite Leg/Hypotenuse  C OSINE (C OS ): Adjacent Leg/Hypotenuse  Example: Find sin A, cos A, sin B, and cos B › sin A = opposite.

Slides:



Advertisements
Similar presentations
Trigonometry Right Angled Triangle. Hypotenuse [H]
Advertisements

8 – 6 The Sine and Cosine Ratios. Sine and Cosine Suppose you want to fine the legs, x and y, in a triangle. You can’t find these values using the tangent.
5/5/ : Sine and Cosine Ratios 10.2: Sine and Cosine Expectation: G1.3.1: Define the sine, cosine, and tangent of acute angles in a right triangle.
Geometry B Bellwork 3) Using the inverse of tangent Find m N to the nearest degree. tan N = = m N = tan -1 (0.6) m N ≈ 31° N RX
Chapter 9. COMPLETE THE RATIO: Tan x = _____ x.
Calculating Sine, Cosine, and Tangent *adapted from Walch Education.
Objective: To use the sine, cosine, and tangent ratios to determine missing side lengths in a right triangle. Right Triangle Trigonometry Sections 9.1.
By: Dasia Miles-Langaigne June 6, 2014
Trigonometry SOH CAH TOA.
8.3 Solving Right Triangles
EXAMPLE 1 Use an inverse tangent to find an angle measure
EXAMPLE 1 Finding Trigonometric Ratios For PQR, write the sine, cosine, and tangent ratios for P. SOLUTION For P, the length of the opposite side is 5.
Trigonometry. Logarithm vs Natural Logarithm Logarithm is an inverse to an exponent log 3 9 = 2 Natural logarithm has a special base or e which equals.
 A trigonometric ratio is a ratio of the lengths of 2 sides of a right triangle.  You will learn to use trigonometric ratios of a right triangle to determine.
8.3 2/21/13 & 2/25/13. Bell Work Use ∆ABC for Exercises 1–3. 1. If a = 8 and b = 5, find c. 2. If a = 60 and c = 61, find b. 3. If b = 6 and c = 10, find.
Honors Geometry Sections 10.1 & 10.2 Trigonometric ratios
A = Cos o x H Cosine Rule To find an adjacent side we need 1 side (hypotenuse) and the included angle. 9 cm 12 cm 60° 75° a a A = Cos ° x H A = Cos 75°
Get a calculator!. Trigonometry Trigonometry is concerned with the connection between the sides and angles in any right angled triangle. Angle.
Warm-Up 3/24-25 What are three basic trigonometric functions and the their ratios? Sine: sin  Cosine: cos  Tangent: tan 
Finding an angle. (Figuring out which ratio to use and getting to use the 2 nd button and one of the trig buttons. These are the inverse functions.) 5.4.
WARM UP Find the following missing values. Find the following missing values. 1)2)
Geometry tan A === opposite adjacent BC AC tan B === opposite adjacent AC BC Write the tangent ratios for A and B. Lesson 8-3 The Tangent Ratio.
The midpoint of is M(-4,6). If point R is (6, -9), find point J.
Trigonometry v=t2uPYYLH4Zo.
Chapter 7.7 Notes: Solve Right Triangles Goal: You will use inverse tangent, sine, and cosine ratios to determine the unknown angle measures of right triangles.
Trigonometric Ratios Trigonometry – The branch of mathematics that deals with the relations between the sides and angles of triangles, and the calculations.
8-3: Trigonometry Objectives To use the sine, cosine, and tangent ratios to determine side lengths and angle measures in right triangles To use the sine,
Chapter 13 Sec 1 Right Triangle Trigonometry 2 of 12 Algebra 2 Chapter 13 Section 1 The ratios of the sides of the right triangle can be used to define.
TRIGONOMETRIC RATIOS Chapter 9.5. New Vocabulary  Trigonometric Ratio: The ratio of the lengths of two sides or a right triangle.  The three basic trigonometric.
Chapter 3-2 Component Vectors. Pythagorean Theorem If two vectors are at a 90 0 angle, use the Pythagorean Theorem to find the resultant vector. C 2 =
Trigonometric Ratios in Right Triangles. Trigonometric Ratios are based on the Concept of Similar Triangles!
Geometry Section 9.5 Trigonometric ratios. The word “trigonometry” comes from two Greek words which mean ___________________ And that is exactly what.
EXAMPLE 4 Using a Sine Ratio Ski Jump
GEOMETRY HELP Use the triangle to find sin T, cos T, sin G, and cos G. Write your answer in simplest terms. sin T = = = opposite hypotenuse.
Set calculators to Degree mode.
TRIGONOMETRY BASIC TRIANGLE STUDY: RATIOS: -SINE -COSINE -TANGENT -ANGLES / SIDES SINE LAW: AREA OF A TRIANGLE: - GENERAL -TRIGONOMETRY -HERO’S.
Section 13.1.b Solving Triangles. 7.) Find the angle Ɵ if cos Ɵ = (Read as “the angle whose cos is:___”) Be sure you know the mode your calculator.
Warm-Up Determine whether the following triangles are acute, right or obtuse. 1. 7, 10, , 8, , 5, 6.
Right Triangle Trigonometry Three Basic Trig Ratios: sin θ = opposite/hypotenuse cos θ = adjacent/hypotenuse tan θ = opposite/adjacent Adjacent Side Hypotenuse.
13.1 Right Triangle Trigonometry
Trigonometric Ratios A RATIO is a comparison of two numbers. For example; boys to girls cats : dogs right : wrong. In Trigonometry, the comparison is between.
Chapter : Trigonometry Lesson 3: Finding the Angles.
You will use the sine and cosine ratio to find the sides and angles of a right triangles Pardekooper.
(1) Sin, Cos or Tan? x 7 35 o S H O C H A T A O Answer: Tan You know the adjacent and want the opposite.
Chapter 13 Right Angle Trigonometry
A C M 5 2. CCGPS Geometry Day 17 ( ) UNIT QUESTION: What patterns can I find in right triangles? Standard: MCC9-12.G.SRT.6-8 Today’s Question: How.
Trig Ratios C 5 2 A M 4. If C = 20º, then cos C is equal to:
9-2 Sine and Cosine Ratios. There are two more ratios in trigonometry that are very useful when determining the length of a side or the measure of an.
Trigonometry Mini-Project Carlos Velazquez 6/4/13 A block.
9.5: Trigonometric Ratios. Vocabulary Trigonometric Ratio: the ratio of the lengths of two sides of a right triangle Angle of elevation: the angle that.
 The study of triangles  Relationship between sides and angles of a right triangle › What is a right triangle? A triangle with a 90 ⁰ angle 90°
SOH-CAH-TOA???? What does the abbreviation above stand for????
Trigonometric Ratios In Trigonometry, the comparison is between sides of a triangle. Used to find a side of a right triangle given 1 side and 1 acute angle.
Adjacent = Cos o x H Cosine Ratio To find an adjacent side we need 1 side (hypotenuse) and the included angle. a = Cos ° x H a = Cos 60° x 9 a = 0.5 x.
[8-3] Trigonometry Mr. Joshua Doudt Geometry pg
Algebra 2 cc Section 7.1 Solve right triangles “Trigonometry” means triangle measurement and is used to solve problems involving triangle. The sides of.
Lesson 8-6 The Sine and Cosine Ratios (page 312) The sine ratio and cosine ratio relate the legs to the hypotenuse. How can trigonometric ratios be used.
How to use sine, cosine, and tangent ratios to determine side lengths in triangles. Chapter GeometryStandard/Goal: 2.2, 4.1.
EXAMPLE 1 Use an inverse tangent to find an angle measure Use a calculator to approximate the measure of A to the nearest tenth of a degree. SOLUTION Because.
Chapter 5 Lesson 1 Trigonometric Ratios in Right Triangles.
Section 9.5: Trigonometric Ratios. trigonometric ratio – a ratio of the lengths of two sides of a right triangle. The three basic trigonometric ratios.
Warm Up Use the following triangles: Find a if b = 10√2
Right Triangles Trigonometry
Angles of Elevation and Depression
You will need a calculator and high lighter!
Hypotenuse hypotenuse opposite opposite adjacent adjacent.
7-4: Trigonometry.
Geometry 9.5 Trigonometric Ratios
Find the missing measures. Write all answers in radical form.
Hypotenuse hypotenuse opposite opposite adjacent adjacent.
Presentation transcript:

 S INE (S IN ): Opposite Leg/Hypotenuse  C OSINE (C OS ): Adjacent Leg/Hypotenuse  Example: Find sin A, cos A, sin B, and cos B › sin A = opposite / hypotenuse = 4 / 5 › cos A = adjacent / hypotenuse = 3 / 5 › sin B = opposite / hypotenuse = 3 / 5 › cos B = adjacent / hypotenuse = 4 / 5

 Your Turn › Find each value › sin P › sin R › cos P › cos R 12 / 13 5 / 13 5 / / 13

 A ski run 8395 feet long has a 20˚ angle of elevation. What is the vertical drop from the top of the run? › Looking for the angle opposite 20˚ › Given the hypotenuse  Use the sin function › sin 20 = x/8395 › 8395  sin 20 = x › ft = x

 You can use the sin -1 and cos -1 buttons on your calculator to find the measure of unknown angles, like we did yesterday with the tan -1 button.  Example: Find the measure of H to the nearest degree. › We have the adjacent side (8) › We have the hypotenuse (9) › Use the cosine function › cos x = 8 / 9 › cos -1 ( 8 / 9 ) = x › 27˚ = x

YYOUR TURN ›F›Find the measure of  R to the nearest degree ›7›71˚

 Assignment › Worksheet #13-5  ThursdayChapter 13 Preview  FridayChapter 13 Review  Next MondayChapter 13 Test  Next TuesdayQuarterly Preview  Next Wed/ThurQuarterly Review  Next Friday3 rd Quarterly Exam

Feedback: Privacy Policy Feedback
Do Not Sell My Personal Information
About project: SlidePlayer Terms of Service

© 2025 SlidePlayer.com. Inc. All rights reserved.