Chapter 8-4 part 1 Trigonometry This lesson has been modified from the original in the following ways: 1.Use of a trig. Table replaces a calculator. Students need access to a trig. table. a) rationale: CST questions are based on table and calculators are not allowed. Cheap accessible calculators can be used for trig. Students better understand the process involved with inverse trig. functions 2. Illustrations have been enlarged. 3. SohCahToa replaces original introduction. Teachers should tell the story of the old chief and his midnight encounter with a coffee table.

Lesson 4 MI/Vocab trigonometry trigonometric ratio sine cosine tangent Find trigonometric ratios using right triangles. Solve problems using trigonometric ratios. Standards 18.0 Students know the definitions of the basic trigonometric functions defined by the angles of a right triangle. They also know and are able to use elementary relationships between them. For example, tan(x) = sin(x)/cos(x), (sin(x))2 + (cos(x))2 = 1. (Key) Standards 19.0 Students use trigonometric functions to solve for an unknown length of a side of a right triangle, given an angle and a length of a side. (Key)

Trig Ratios Compares the lengths of two sides of a right triangle Sine(sin) Cosine(cos) Tangent(tan)

Given Rt. Triangle ABC Given  A –Side a is the Opposite –Side b is the Adjacent –Side c is the Hypotenuse Given  B –Side a is the Adjacent –Side b is the Opposite –Side c is still the Hypotenuse b a c C A B

Trig Ratios SOH-CAH-TOA Opposite Opp Hypotenuse Hyp Sin == Adjacent Adj Hypotenuse Hyp Cos == Opposite Opp Adjacent Adj Tan ==

Given Rt. Triangle ABC Given  A  Sin A =  Cos A=  Tan A= b a c C A B Given  B Sin B = Cos B = Tan B = SOH-CAH-TOA

Given Rt. Triangle ABC Given  A  Sin A =  Cos A=  Tan A= Given  B Sin B = Cos B = Tan B = SOH-CAH-TOA C A B

A.A B.B C.C D.D Lesson 4 CYP1 A. Find sin A. A. B. C. D.

A.A B.B C.C D.D Lesson 4 CYP1 B. Find cos A. A. B. C. D.

A.A B.B C.C D.D Lesson 4 CYP1 C. Find tan A. A. B. C. D.

A.A B.B C.C D.D Lesson 4 CYP1 D. Find sin B. A. B. C. D.

A.A B.B C.C D.D Lesson 4 CYP1 E. Find cos B. A. B. C. D.

A.A B.B C.C D.D Lesson 4 CYP1 F. Find tan B. A. B. C. D.

Angle Measure SinCosTan Angle Measure SinCosTan Using a Trig. Table Find the Sine Cosine and Tangent of

Lesson 4 CYP2 1.A 2.B 3.C 4.D A B C D A. Use your trig. table to find sin 48° to the nearest ten thousandth.

Lesson 4 CYP2 1.A 2.B 3.C 4.D A B C D B. Use your trig. table to find cos 85° to the nearest ten thousandth.

Finding Missing Side Lengths Decide which Trig function to use based on the given angle measure the given side and the unknown side Substitute the given information and the unknown variable into the function’s equation Solve for the variable (cross-multiply if necessary) Calculate

Given Rt. Triangle ABC Solve for x y x 10 C A B 32 o Opp Hyp SOH-CAH-TOA

Given Rt. Triangle ABC Solve for y y x 10 C A B 32 o Adj Hyp SOH-CAH-TOA

Given Rt. Triangle ABC Solve for x y x 3 C A B 27 o Adj Opp SOH-CAH-TOA

Given Rt. Triangle ABC Solve for y y x 3 C A B 27 o Adj Hyp SOH-CAH-TOA 1

Given Rt. Triangle ABC Solve for x x 12 C A B 58 o AdjOpp SOH-CAH-TOA 1

Homework Chapter 8-4 Pg 460 1,2,14-17,29- 37,44,46,47,48 Bring Calculators from now on!!!

Chief SohCahToa The Amazing Legend of…

Chief SohCahToa Once upon a time there was a wise old Native American Chief named Chief SohCahToa. He was named that due to an chance encounter with his coffee table in the middle of the night. He woke up hungry, got up and headed to the kitchen to get a snack. He did not turn on the light and in the darkness, stubbed his big toe on his coffee table….