1 Press Ctrl-A ©G Dear2008 – Not to be sold/Free to use Sine Ratio Stage 4 Year 9.

Slides:



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

1 Press Ctrl-A ©G Dear2008 – Not to be sold/Free to use Tangent Ratio Stage 4 Year 9.
Trig Graphs. y = sin x y = cos x y = tan x y = sin x + 2.
Add hypotenuse, the three proportions, Pythagorean Thm. and Converse(obtuse, acute), multiply fractions vs. proportions, and formulas,
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.
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
Trigonometry Chapters Theorem.
Trigonometry-5 Examples and Problems. Trigonometry Working with Greek letters to show angles in right angled triangles. Exercises.
Basic Trigonometry.
Trigonometry-6 Finding Angles in Triangles. Trigonometry Find angles using a calculator Examples to find sin, cos and tan ratios of angles Examples to.
5.4 Trig. Ratios Trigonometer Trigon- Greek for triangles Metric- Greek for Measure.
Trigonometry Unit 2: 2-dimensional Motion From:
A B C Warm UP What side is The hypotenuse? What side is opposite  A?
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°
Press Ctrl-A ©G Dear2008 – Not to be sold/Free to use Cosine Rule Angles Stage 6 - Year 12 General Mathematic (HSC)
There are 3 kinds of trigonometric ratios we will learn. sine ratio cosine ratio tangent ratio Three Types Trigonometric Ratios.
Warm-Up 3/24-25 What are three basic trigonometric functions and the their ratios? Sine: sin  Cosine: cos  Tangent: tan 
1 One Steppers Press Ctrl-A G Dear ©2009 – Not to be sold/Free to use Stage 4 Year 7.
Warmup: What is wrong with this? 30 ⁰. 8.3 and 8.4 Trigonometric Ratios.
The midpoint of is M(-4,6). If point R is (6, -9), find point J.
1 Press Ctrl-A ©G Dear2008 – Not to be sold/Free to use Introduction Applied Mathematics Preliminary Stage 6.
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.
Trig Review: PRE-AP Trigonometry Review Remember right triangles? hypotenuse θ Opposite side Adjacent side Triangles with a 90º angle.
Trigonometric Ratios in Right Triangles. Trigonometric Ratios are based on the Concept of Similar Triangles!
Introduction to Trigonometry What is Trigonometry? Trigonometry is the study of how the sides and angles of a triangle are related to each other. It's.
Review of Trig Ratios 1. Review Triangle Key Terms A right triangle is any triangle with a right angle The longest and diagonal side is the hypotenuse.
1 Press Ctrl-A ©G Dear2008 – Not to be sold/Free to use Cosine Ratio Stage 4 Year 9.
Press Ctrl-A ©G Dear2008 – Not to be sold/Free to use Radial Survey Stage 6 - Year 12 General Mathematic (HSC)
BASIC GEOMETRY Section 8.2: Trigonometric Ratios
8.4 Trigonometric Ratios.
Right Triangle Trigonometry Three Basic Trig Ratios: sin θ = opposite/hypotenuse cos θ = adjacent/hypotenuse tan θ = opposite/adjacent Adjacent Side Hypotenuse.
Finding a Missing Angle of a Right Triangle. EXAMPLE #1  First: figure out what trig ratio to use in regards to the angle.  Opposite and Adjacent O,A.
Warm- up What do you remember about right triangles?
World 5-1 Trigonometric Ratios. Recall that in the past finding an unknown side of a right triangle required the use of Pythagoras theorem. By using trig.
Chapter : Trigonometry Lesson 3: Finding the Angles.
1 Multiplication By Decimals Stage 4 Years 7 & 8 Press Ctrl-A ©2009 G Dear – Not to be sold/Free to use.
Press Ctrl-A ©G Dear2008 – Not to be sold/Free to use Finding a Side Stage 6 - Year 12 General Mathematic (HSC)
TRIGONOMETRY Lesson 2: Solving Right Triangles. Todays Objectives Students will be able to develop and apply the primary trigonometric ratios (sine, cosine,
You will use the sine and cosine ratio to find the sides and angles of a right triangles Pardekooper.
Press Ctrl-A ©G Dear2008 – Not to be sold/Free to use Sine Rule - Side Stage 6 - Year 12 General Mathematic (HSC)
(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.
Lesson 46 Finding trigonometric functions and their reciprocals.
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:
9-1 Tangent Ratio 9-2 Sine and Cosine Ratio Learning Target: I will be able to solve problems using the tangent, sine, and cosine ratios. Goal 1.01.
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.
1 Plotting Points Using a Table Press Ctrl-A ©2009 G Dear – Not to be sold/Free to use Stage 4 Years 7 & 8.
SOH-CAH-TOA???? What does the abbreviation above stand for????
9-1 Tangent Ratio 9-2 Sine and Cosine Ratio Learning Target: I will be able to solve problems using the tangent, sine, and cosine ratios. Goal 1.01.
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 Part 2: Inverse Trigonometric Functions.
[8-3] Trigonometry Mr. Joshua Doudt Geometry pg
Date: Topic: Trigonometric Ratios (9.5). Sides and Angles x The hypotenuse is always the longest side of the right triangle and is across from the right.
Trig Functions – Part Pythagorean Theorem & Basic Trig Functions Reciprocal Identities & Special Values Practice Problems.
Trigonometry Lesley Soar Valley College Objective: To use trigonometric ratios to find sides and angles in right-angled triangles. The Trigonometric.
Chapter 5 Lesson 1 Trigonometric Ratios in Right Triangles.
1 Press Ctrl-A ©G Dear 2009 – Not to be sold/Free to use Trigonometry Finding Sides Stage 6 - Year 11 General Mathematics Preliminary.
©G Dear2008 – Not to be sold/Free to use
…there are three trig ratios
You will need a calculator and high lighter!
…there are three trig ratios
Hypotenuse hypotenuse opposite opposite adjacent adjacent.
©G Dear2008 – Not to be sold/Free to use
Right Triangle Ratios Chapter 6.
Right Triangle Ratios Chapter 6.
©G Dear2008 – Not to be sold/Free to use
Hypotenuse hypotenuse opposite opposite adjacent adjacent.
©G Dear2008 – Not to be sold/Free to use
Trigonometric Ratios Geometry.
…there are three trig ratios
Presentation transcript:

1 Press Ctrl-A ©G Dear2008 – Not to be sold/Free to use Sine Ratio Stage 4 Year 9

2 Hypotenuse Opposite Opposite Click Sin θ = OppositeHypotenuse θ θ Trig Ratios

Sin θ = OppositeHypotenuseP QR 5 Sin P = Sin R = 5 13 Trig Ratios

4 26 P Q R 10 Sin A = A B 5 C Sin P = = 22222222 Sin C = 5 13 Sin R = = 5 13 22222222 24 Trig Ratios Sin θ = OppositeHypotenuse

o m sin 30 o = m 6 6x x6 m = 6 x sin 30 o = 3 Use your Calculator! Trig Ratios Sin θ = OppositeHypotenuse

o d sin 60 o = d 10 10xx10 10 x sin 60 o ≈ 8.66 Use your Calculator! d = Trig Ratios Sin θ = OppositeHypotenuse

7 k 40 o 6 sin 40 o = 6 k kx xk = 6 k x sin 40 o ≈ 9.33 Use your Calculator!  Sin 40 o  Sin 40 o k = 6  sin 40 o Trig Ratios Sin θ = OppositeHypotenuse

8 12 zozozozo 6 sin z o = 6 12 zo =zo =zo =zo = sin -1 ( ) Use your Calculator! = 30 o 612 Trig Ratios Sin θ = OppositeHypotenuse

9 15 momomomo 5 sin m o = 5 15 mo =mo =mo =mo = sin -1 ( ) Use your Calculator! ≈ 20 o 515 To nearest whole degree Trig Ratios Sin θ = OppositeHypotenuse

10 S Some O Old H Hags C Can A Always H Hide T Their O Old A Age S Sin O Opposite H Hypotenuse C Cos A Adjacent H Hypotenuse T Tan O Opposite A Adjacent