We think you have liked this presentation. If you wish to download it, please recommend it to your friends in any social system. Share buttons are a little bit lower. Thank you!
Presentation is loading. Please wait.
Published byAlicia Knopp
Modified about 1 year ago
© Boardworks Ltd of 43 θ OPPOSITEOPPOSITE H Y P O T E N U S E A D J A C E N T The three trigonometric ratios Sin θ = Opposite Hypotenuse S O H Cos θ = Adjacent Hypotenuse C A H Tan θ = Opposite Adjacent T O A Remember: S O H C A H T O A
© Boardworks Ltd of 43 Finding side lengths If we are given one side and one acute angle in a right-angled triangle we can use one of the three trigonometric ratios to find the lengths of other sides. For example, 56° x 12 cm Find x to 2 decimal places. We are given the hypotenuse and we want to find the length of the side opposite the angle, so we use: sin θ = opposite hypotenuse sin 56° = x 12 x = 12 × sin 56° = 9.95 cm
© Boardworks Ltd of 43 Finding side lengths A 5 m ladder is resting against a wall. It makes an angle of 70° with the ground. 5 m 70° x What is the distance between the base of the ladder and the wall? We are given the hypotenuse and we want to find the length of the side adjacent to the angle, so we use: cos θ = adjacent hypotenuse cos 70° = x 5 x = 5 × cos 70° = 1.71 m (to 2 d.p.)
© Boardworks Ltd of 43 Finding side lengths
© Boardworks Ltd of 43 The inverse of sin sin θ = 0.5, what is the value of θ ? To work this out use the sin –1 key on the calculator. sin –1 0.5 =30° sin –1 is the inverse of sin. It is sometimes called arcsin. 30° 0.5 sin sin –1
© Boardworks Ltd of 43 The inverse of cos Cos θ = 0.5, what is the value of θ ? To work this out use the cos –1 key on the calculator. cos –1 0.5 =60° Cos –1 is the inverse of cos. It is sometimes called arccos. 60° 0.5 cos cos –1
© Boardworks Ltd of 43 The inverse of tan tan θ = 1, what is the value of θ ? To work this out use the tan –1 key on the calculator. tan –1 1 =45° tan –1 is the inverse of tan. It is sometimes called arctan. 45° 1 tan tan –1
© Boardworks Ltd of 43 Finding angles We are given the lengths of the sides opposite and adjacent to the angle, so we use: tan θ = opposite adjacent tan θ = 8 5 = 57.99° (to 2 d.p.) θ 5 cm 8 cm θ = tan –1 (8 ÷ 5) Find θ to 2 decimal places.
© Boardworks Ltd of 43 Finding angles
The inverse trigonometric functions The reciprocal trigonometric functions Trigonometric identities Examination-style question Contents © Boardworks Ltd.
Trigonometry. Sides and Angles Basic trigonometry is about things to do with the different ANGLES in a right angle triangle Look at the angle labeled.
Trigonometry by P Rowell Tile Hill Wood School. Triangles -the basics In any triangle the three angles add up to 180° One of the angles in a right angle.
Right AngledTriangles Right Angled Triangles The key points.
Solving Right Triangles Essential Question How do I solve a right triangle?
Measurement Pythagorean Relationship 2 (Finding the length of the Hypotenuse)
8.1: Right Triangles Pythagorean Theorem Properties of Special Right Triangles.
Measurement Pythagorean Relationship 3 (Finding the length of an unknown leg)
Copyright © Cengage Learning. All rights reserved. 4.3 Right Triangle Trigonometry.
Page 1 TRIGONOMETRY. Page 2 TrigonometryAn Introduction Trigonometry is the study of the relationship between the angles and the sides of triangles. Example:
Copyright © Cengage Learning. All rights reserved. 4.7 Inverse Trigonometric Functions.
FeatureLesson Geometry Lesson Main For each triangle, find (a) the length of the leg opposite B and (b) the length of the leg adjacent to B. (For help,
Introducing Trigonometry. 30 º Hypotenuse Adjacent Opposite.
Notes # ____. trigonometry trigonometry : the study of the properties of triangles trigonometric ratio trigonometric ratio : ratio of measures of two.
CHAPTER 4 Trigonometric Functions. 4.1 Angles & Radian Measure Objectives –Recognize & use the vocabulary of angles –Use degree measure –Use radian measure.
1 Right Triangle Trigonometry Pre-Calculus. Todays Objective Review right triangle trigonometry from Geometry and expand it to all the trigonometric functions.
The Ambiguous Case of the Law of Sines. This is the SSA case of an oblique triangle. SSA means you are given two sides and the angle opposite one of them.
. . CONSTRUCTION OF A RIGHT TRIANGLE IF THE ONE ANGLE OF A TRIANGLE IS 90,IT IS CALLED RIGHT TRIANGLE.
Trigonometry Ratios. Example 1 Write the Trig Ratio for each of the following ( soh, cah, toa)
4.4 – Prove Triangles Congruent by SAS and HL Consider a relationship involving two sides, and the angle they form, their included angle. Any time you.
Trigonometric Functions The Unit Circle. Definition: A circle whose center is the origin and whose radius has a length of one. Based on the definition,
Unit 2 - Right Triangles and Trigonometry Chapter 8.
Topic 1.3 Extended B - Components of motion Up to now we have considered objects moving in one dimension. However, most objects move in more than one.
Holt Geometry 8-2 Trigonometric Ratios 8-2 Trigonometric Ratios Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson.
Trigonometry Basics Right Triangle Trigonometry.
© Boardworks Ltd of 84 KS3 Mathematics S8 Perimeter, area and volume.
Day 7 In geometry, a median of a triangle is a line segment joining a vertex to the midpoint of the opposing side. Every triangle has exactly three medians;
Determining signs of Trig Functions (Pos/Neg) x y Last class we found trig values using an x-y coordinate. Not all trig values are positive We can determine.
Trigonometry. A review of basic trigonometry SOH CAH TOA ‘Opposite’ and ‘adjacent’ are defined by the angle that is being considered. opposite adjacent.
© 2016 SlidePlayer.com Inc. All rights reserved.