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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 = = 22222222 Sin C = 5 13 Sin R = = 5 13 22222222 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
1 Press Ctrl-A ©G Dear2008 – Not to be sold/Free to use Cosine Ratio Stage 4 Year 9.
1 Press Ctrl-A ©G Dear2008 – Not to be sold/Free to use Tangent Ratio Stage 4 Year 9.
1 Press Ctrl-A ©G Dear2008 – Not to be sold/Free to use Introduction Applied Mathematics Preliminary Stage 6.
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Press Ctrl-A ©G Dear2008 – Not to be sold/Free to use Sine Rule - Side Stage 6 - Year 12 General Mathematic (HSC)
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.
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Press Ctrl-A ©G Dear2008 – Not to be sold/Free to use Finding a Side 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.
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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.
Similarity of any right triangle with the same acute measure. All 3 of the triangles are similar Their sides are in proportion We can write these proportions.
Right Triangle Trigonometry Three Basic Trig Ratios: sin θ = opposite/hypotenuse cos θ = adjacent/hypotenuse tan θ = opposite/adjacent Adjacent Side Hypotenuse.
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1 Plotting Points Using a Table Press Ctrl-A ©2009 G Dear – Not to be sold/Free to use Stage 4 Years 7 & 8.
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.
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.
Trigonometric Ratios in Right Triangles. Trigonometric Ratios are based on the Concept of Similar Triangles!
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.
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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.
A C B What side is The hypotenuse? What side is opposite A? What side is adjacent to A? What side is opposite B? What side is adjacent to B? Line.
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Press Ctrl-A ©G Dear2008 – Not to be sold/Free to use Radial Survey Stage 6 - Year 12 General Mathematic (HSC)
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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.
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Chapter : Trigonometry Lesson 3: Finding the Angles.
Add hypotenuse, the three proportions, Pythagorean Thm. and Converse(obtuse, acute), multiply fractions vs. proportions, and formulas,
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The midpoint of is M(-4,6). If point R is (6, -9), find point J.
8.4 Trigonometric Ratios. The word trigonometry comes from two Greek terms, trigon (triangle) and metron (measure). A trigonometric ratio is a ratio.
A = Cos o x H Cosine Rule 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 9 A = 4.5.
Trig Graphs. y = sin x y = cos x y = tan x y = sin x + 2.
Trigonometry Chapters Theorem.
Trig Review: PRE-AP Trigonometry Review Remember right triangles? hypotenuse θ Opposite side Adjacent side Triangles with a 90º angle.
1 Multiplication By Decimals Stage 4 Years 7 & 8 Press Ctrl-A ©2009 G Dear – Not to be sold/Free to use.
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 Cosine Rule Angles Stage 6 - Year 12 General Mathematic (HSC)
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