Calculating Sine, Cosine, & Tangent (5.9.1)

Slides:

Advertisements

Similar presentations

Objective - To use basic trigonometry to solve right triangles.

Advertisements

Splash Screen. Lesson Menu Five-Minute Check (over Lesson 8–3) NGSSS Then/Now New Vocabulary Key Concept: Trigonometric Ratios Example 1: Find Sine, Cosine,

Geometry Notes Lesson 5.3C Trigonometry T.2.G.6 Use trigonometric ratios (sine, cosine, tangent) to determine lengths of sides and measures of angles in.

Solving Right Triangles Given certain measures in a right triangle, we often want to find the other angle and side measures. This is called solving the.

Calculating Sine, Cosine, and Tangent *adapted from Walch Education.

Trigonometry Chapters Theorem.

Solving Right Triangles

60º 5 ? 45º 8 ? Recall: How do we find “?”. 65º 5 ? What about this one?

45 ⁰ 45 – 45 – 90 Triangle:. 60 ⁰ 30 – 60 – 90 Triangle: i) The hypotenuse is twice the shorter leg.

Solve Right Triangles Ch 7.7. Solving right triangles What you need to solve for missing sides and angles of a right triangle: – 2 side lengths – or –

Bellringer Angle A (or θ) = a = 1, b =, and c = 2.

8.3 Solving Right Triangles

7.6 Law of Sines. Use the Law of Sines to solve triangles and problems.

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.

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.

Sine, Cosine and Tangent Ratios Objective Students will be able to use sine, cosine, and tangent ratios to determine side lengths in triangles.

Lesson 1: Primary Trigonometric Ratios

Geometry Notes Lesson 5.3B Trigonometry

The Basics State the RatioSidesAnglesReal-Life

Friday, February 5 Essential Questions

Geometry One is always a long way from solving a problem until one actually has the answer. Stephen Hawking Today: ACT VOCAB CHECK 8.4 Cont. Practice.

Warmup: What is wrong with this? 30 ⁰. 8.3 and 8.4 Trigonometric Ratios.

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.

SECTION 8.4 TRIGONOMETRY. The word trigonometry comes from two greek terms, trigon, meaning triangle, and metron, meaning measure. a trigonometric ratio.

Geometry One is always a long way from solving a problem until one actually has the answer. Stephen Hawking Today: ACT VOCAB CHECK 9.6 Instruction Practice.

Warm – up: Find the missing measures. Write all answers in radical form. 45° x w 7 60° 30° 10 y z.

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.

7.2 Finding a Missing Side of a Triangle using Trigonometry

5.3 Apply the SINE and COSINE ratios We will look at the TANGENT ratio tomorrow!

TRIGONOMETRY Lesson 2: Solving Right Triangles. Todays Objectives Students will be able to develop and apply the primary trigonometric ratios (sine, cosine,

Solve Right Triangles Ch 7.7. Solving right triangles What you need to solve for missing sides and angles of a right triangle: – 2 side lengths – or –

Right Triangle Trigonometry Three Basic Trig Ratios: sin θ = opposite/hypotenuse cos θ = adjacent/hypotenuse tan θ = opposite/adjacent Adjacent Side Hypotenuse.

© 2010 Pearson Prentice Hall. All rights reserved. CHAPTER 10 Geometry.

8-4 Trigonometry, day 2 You used the Pythagorean Theorem to find missing lengths in right triangles. Find trigonometric ratios using right triangles. Use.

Find the missing measures. Write all answers in radical form. 45° x w 7 60° 30° 10 y z.

Right Triangle Trigonometry

TRIGONOMETRY Lesson 2: Solving Right Triangles. Todays Objectives Students will be able to develop and apply the primary trigonometric ratios (sine, cosine,

Splash Screen. Then/Now You used the Pythagorean Theorem. Find trigonometric ratios of angles. Use trigonometry to solve triangles.

TRIGONOMETRIC RATIOS The Trigonometric Functions we will be looking at SINE COSINE TANGENT.

Solving Equations with Trig Functions. Labeling a right triangle A.

Splash Screen. Then/Now You used the Pythagorean Theorem to find missing lengths in right triangles. Find trigonometric ratios using right triangles.

5-Minute Check 1 Find x and y. A. B. C. D. Starter(s):

Section 9.5: Trigonometric Ratios. trigonometric ratio – a ratio of the lengths of two sides of a right triangle. The three basic trigonometric ratios.

April 21, 2017 The Law of Sines Topic List for Test

Find the values of the variables.

Trigonometry Ratios in Right Triangles

May 9, 2003 Sine and Cosine Ratios LESSON 8-4 Additional Examples

7-6 Sine and Cosine of Trigonometry

Angles of Elevation and Depression

Agenda: Warmup Notes/practice – sin/cos/tan Core Assessment 1 Monday

Inverse Trigonometric Functions

Objectives Find the sine, cosine, and tangent of an acute angle.

Bell Ringer Please make sure you have turned in your homework (WB pgs ) in the tray. Please answer the following questions using your notes from.

Warm – up: Find the missing measures. Write all answers in radical form. 30° 45° x 7 10 z 45° w 60° y.

7.4 - The Primary Trigonometric Ratios

CHAPTER 10 Geometry.

Hypotenuse hypotenuse opposite opposite adjacent adjacent.

Geometry/TRIG Name: _________________________

LESSON 8–4 Trigonometry.

Trigonometry Ratios in Right Triangles

Solve Right Triangles Mr. Funsch.

Review these 1.) cos-1 √3/ ) sin-1-√2/2 3.) tan -1 -√ ) cos-1 -1/2

Solving Right Triangles -- Trig Part III

Review: Find the missing measures. Write all answers in radical form.

Right Triangle Trigonometry

Geometry Section 7.7.

Trigonometric Ratios Geometry.

Reviewing Trig Ratios 7.4 Chapter 7 Measurement 7.4.1

Presentation transcript:

Calculating Sine, Cosine, & Tangent (5.9.1) June 6th, 2016

Don’t Forget... *The Pythagorean Theorem can be used to find a missing side length in a right triangle, as long as you know the other two side lengths.

Finding Trigonometric Ratios Ex. 1: In , is a right angle and . What are the sine and tangent of ? Write your answers as fractions and decimals. (Draw a labeled diagram of the triangle first.)

hypotenuse adjacent 5 opposite

Using Trigonometric Ratios to Find Missing Side Lengths in Right Triangles Ex. 2: At a certain time of day, a telephone pole casts a shadow that forms an angle of with the ground. The shadow has length 35 feet. How tall is the telephone pole? (Round answers to the nearest thousandth).

Using Trigonometric Ratios to Find Missing Angle Measures in Right Triangles *The inverse trigonometric functions and can cancel out the original trigonometric function to solve for the angle measure inside of the function.

Ex. 3: Find the value of x.

Ex. 4: Solve the right triangle described. ( Ex. 4: Solve the right triangle described. (*Solving a triangle means to find every missing side length and every missing angle measure.) , where is a right angle, KL=19 cm, and KJ=15 cm.

Ex. 5: Solve the right triangle described. , where is a right angle, , and PN=4 in.