SOHCAHTOA.  Write down everything you know about triangles.  Include any vocabulary related to triangles that you may have learned.  Include Diagrams.

Slides:



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

Trigonometric Ratios Please view this tutorial and answer the follow-up questions on loose leaf to turn in to your teacher.
Geometry 9.5 Trigonometric Ratios May 5, 2015Geometry 9.5 Trigonometric Ratios w/o Calculator2 Goals I can find the sine, cosine, and tangent of an acute.
Lesson 9-1 & 9-2: Trigonometry of Right Triangles (Sine, Cosine, Tangent) SOH-CAH-TOA.
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.
Objective: To use the sine, cosine, and tangent ratios to determine missing side lengths in a right triangle. Right Triangle Trigonometry Sections 9.1.
Trigonometry Chapters Theorem.
Basic Trigonometry.
Trigonometry can be used for two things: 1.Using 1 side and 1 angle to work out another side, or 2.Using 2 sides to work out an angle.
Trigonometry (RIGHT TRIANGLES).
Trigonometry-6 Finding Angles in Triangles. Trigonometry Find angles using a calculator Examples to find sin, cos and tan ratios of angles Examples to.
By: Dasia Miles-Langaigne June 6, 2014
Warm Up for Section 1.2 Simplify: (1). (2). (3). There are 10 boys and 12 girls in a Math 2 class. Write the ratio of the number of girls to the number.
Sine, Cosine and Tangent Ratios Objective Students will be able to use sine, cosine, and tangent ratios to determine side lengths in triangles.
A B C Warm UP What side is The hypotenuse? What side is opposite  A?
Geometry Notes Lesson 5.3B Trigonometry
Unit 1 – Physics Math Algebra, Geometry and Trig..
1 Trigonometry Basic Calculations of Angles and Sides of Right Triangles.
1 Trigonometry Basic Calculations of Angles and Sides of Right Triangles.
Solving Right Triangles
Unit J.1-J.2 Trigonometric Ratios
 Students will recognize and apply the sine & cosine ratios where applicable.  Why? So you can find distances, as seen in EX 39.  Mastery is 80% or.
Warmup: What is wrong with this? 30 ⁰. 8.3 and 8.4 Trigonometric Ratios.
Section 8.5 Tangent Ratio. What is Trigonometry ? The study of triangles and their measurements.
Warm- Up 1. Find the sine, cosine and tangent of  A. 2. Find x. 12 x 51° A.
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.
Finish Calculating Ratios from last Friday Warm UP: Find x: 1. x 2. L ║ M 3. Read and highlight “Trigonometry” 22April 2013 Geometry 144º 7 6 x 5 L M.
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.
7.2 Finding a Missing Side of a Triangle using Trigonometry
TRIGONOMETRY BASIC TRIANGLE STUDY: RATIOS: -SINE -COSINE -TANGENT -ANGLES / SIDES SINE LAW: AREA OF A TRIANGLE: - GENERAL -TRIGONOMETRY -HERO’S.
Trigonometric Ratios and Their Inverses
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.
Trigonometry SOHCAHTOA.
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.
Introduction to Trigonometry Part 1
Warm- up What do you remember about right triangles?
Trigonometry Basics Right Triangle Trigonometry.
1 Trigonometry Basic Calculations of Angles and Sides of Right Triangles.
Objective: Students will be able to… Use the sine, cosine, and tangent ratios to determine missing side lengths and angle measures in a right triangle.
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.
4-57.  To find out how high Juanisha climbed up stairs, you need to know more about the relationship between the ratios of the sides of a right triangle.
Trigonometry Ratios.
7.4 Trigonometry What you’ll learn:
You will use the sine and cosine ratio to find the sides and angles of a right triangles Pardekooper.
Right Triangle Trigonometry Ratios Must label the sides B A C From the marked angle… Hypotenuse- across from the right angle Adjacent – next to.
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.
Lesson 43: Sine, Cosine, and Tangent, Inverse Functions.
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.
A C M If C = 20º, then cos C is equal to: A. sin 70 B. cos 70 C. tan 70.
LC8: TRIGONOMETRY 8C, 8D. MS. JELLISON, WHAT ARE WE DOING TODAY? 8C Label the sides of a right triangle as opposite, adjacent, and hypotenuse. 8D Apply.
Trigonometry can be used for two things: 1.Using 1 side and 1 angle to work out another side, or 2.Using 2 sides to work out an angle.
A Quick Review ► We already know two methods for calculating unknown sides in triangles. ► We are now going to learn a 3 rd, that will also allow us to.
Chapter 5 Lesson 1 Trigonometric Ratios in Right Triangles.
Geometry 9.5 Trigonometric Ratios.
TRIGONOMETRY.
Trigonometric Functions
How do we use trig ratios?
Trigonometry Ratios in Right Triangles
Geometry Unit 8-5: The Tangent Ratio.
Right Triangle Trigonometry
You will need a calculator and high lighter!
A little pick-me-up.
Basic Trigonometry.
Trigonometry Ratios in Right Triangles
Solve for the missing side.
Geometry 9.5 Trigonometric Ratios
Trigonometric Ratios Geometry.
Presentation transcript:

SOHCAHTOA

 Write down everything you know about triangles.  Include any vocabulary related to triangles that you may have learned.  Include Diagrams.  Be Creative….

I like the Nick Name RATS!

 Imagine the pitcher stands at the pitcher’s mound at one of the acute angles. S/he throws the ball to the side which is opposite to him/her. Pitcher’s Mound opposite

 From the opposite side, the player throws the ball to the player at the hypotenuse. 1 1 Pitcher’s Mound opposite hypoteneuse

 The player at the hypotenuse throws the ball to the last side of the triangle which is the adjacent. 1 1 Pitcher’s Mound Opposite Hypoteneuse 4 4 Adjacent

 Every right angled triangle has three sides labelled from a reference angle. Hypoteneuse Opposite Adjacent Reference Angle

 What happens if we move the reference angle?  Discuss this with a partner? How does this change the labels on the sides? Reference Angle

 The adjacent and the opposite are switched!  The Hypotenuse stays the same! Reference Angle Adjacent Hypotenuse—doesn’t change! Opposite

 Label all the three sides from the reference angle. H H A A O O

A A

Here is a quick way to remember the sides that correspond to each ratio. S O H C A H T O A

 Have you noticed three buttons on your calculator? Sin Cos Tan These buttons relate to the three trig ratios we have shown from the RATS.

 The calculator can calculate the ratio for any given angle instantly. Sin Cos Tan Find the sin 98 °. You may need to determine if you press the sin button or enter 98 first. Try this on your calculator: Answer is:

 Check to see if your calculator is in the wrong mode.  ✔ Right Mode: Degree, D, Deg  ✗ Wrong Modes: Grad, Rad  Find your Mode Button to change it to Degrees and try the question again. Mode

Sin Cos Tan Find the following ratios using your calculator to 4 decimals: sin 45°= cos 60°= tan 57°=

Sin-1 Cos-1 Tan-1 Find the above buttons on your calculator. They may be above your sin/cos/tan keys. You may need to use a Second Function Key or another key to access these additional functions on your calculator. These buttons help you find the angle if you are given the trig ratio. I call this ‘going backwards’.

Sin-1 Cos-1 Tan-1 Let’s try the following example. Find the angle if: Method 1: Enter 4 ⁄ 5 on your calculator and enter second function sin Method 2: Enter second function sin ( 4 ⁄ 5) on your calculator ANSWER: degrees

 What are the three trig ratios from the reference angle

 Find the three ratios from the following triangle ✔ ✔

√√ 715 ✔A✔A ✔A✔A S O H C A H T O A S O H C A H T O A Starting at the reference angle decide which two sides you have. Pick the trig ratio that uses those two sides. O H

 Ask yourself: What sides do I have?  Which Trig Ratio uses those two sides! 6 25 ✔B✔B ✔B✔B

36 25 ✔C✔C ✔C✔C Ask yourself: What sides do I have? Which Trig Ratio uses those to sides!

 Find the missing side x. 56° 20 X

 Have: Hypoteneuse  Need: Adjacent  Use the Cosine Ratio 56° 20 X

56° 20 X

56° 20 X

 Find the missing side x. 35° x 12

What is the side you have and what is the side you need? Have: Opposite Need: Hypotenuse Use the Sine Ratio 35° x 12

 The ratio that uses both the O and the H is the sin ratio. 35° X is the hypotenuse12 is the opposite side

 Now we can fill in the ratio: 35° X12

 Now we can fill in the ratio: Solve for x in the above equation by using the ‘Switcheroo’

 If the side you are missing is in the NUMERATOR such as: Then multiply the two values together x=sin 43 x 12

 If the side you are missing is in the DENOMINATOR such as: Then use the ‘switcheroo’ to switch the cos 43 and the x Answer would be 7÷(cos 43)

 Case 1: Multiply ×  Case 2: Switcheroo ÷

II hope this was everything you needed to know about trigonometry!