Unit 3 Trigonometry. Topic: Review of Necessary Skills

Transcription

1 Lesson18.notebook Unit 3 Trigonometry Topic: Review of Necessary Skills Learning Goal: I can successfully use Pythagorean theorem and the primary trigonometric ratios and extend them to real world applications. Similar Triangles Primary Trigonometric Ratios 1

2 Lesson18.notebook Secondary Trigonometric Ratios Example: Determine the missing value. 2

3 Lesson18.notebook Example: Determine the missing value. Example: Determine the missing value. 3

4 Lesson18.notebook Example: While standing on a cliff 45 m high, Erin could see a ship located out on the lake. She measured the angle of decline to view the ship at 35 degrees. Determine how far from shore the boat is located. Homework: pg 53, # 1 4, 5 7, 9, 10 Handout 4

5 Lesson19.notebook Topic: Special Triangles Learning Goal: I can construct and determine the exact value of special angles by applying the values found in the special triangles. Two Basic Special Triangles Example: Determine the exact value of the following. 1

6 Lesson19.notebook Other "Special" Triangles Example: If sina = 8/13, determine the exact value of tanb. Example: If cosa = 3/7, determine the exact value of sina. Homework: Handout 2

7 Lesson20.notebook Topic: CAST Rule Learning Goal: I can explain and apply the CAST rule to help determine the value of the angle theta. The CAST Rule Terminology: Recall: 1

8 Lesson20.notebook Example: Determine the exact value of all 3 trig. ratios. 1) θ = 60 2) θ = 120 3) θ = 330 4) θ = 150 Example: Determine the exact value of the following. 2

9 Lesson20.notebook Homework: pg. 56, # Handout 3

10 Lesson21.notebook Topic: Applying the CAST Rule Learning Goal: I can apply the CAST Rule to equations involving trigonometric equations and solve for all values of θ, where 0< θ < 360. Example: Solve for all values of θ, where 0 θ ) 6cosθ = 3 3 2) 4 + sinθ = 6 3) cosθ = 0 4) 3 3 = 1 + tanθ 3 1

11 Lesson21.notebook 5) 1.68 = 2sinθ 6) 12 + tanθ = 9.75 Homework: pg. 57, Even questions pg. 59, Even questions 2

12 Lesson22.notebook Topic: Multi Step Two Dimensional Trigonometric Problems Learning Goal: I can use my understanding of the primary trig ratios, Sine Law and Cosine Law to solve questions that require at least 2 steps to solve. Example: Determine the missing value. 1) 40' 15 m x 25' Example: Determine the area of the following triangle. 1) 15' 20 m x 30' 1

13 Lesson22.notebook 2) 8 m 50' 70' Example: Determine the length of the support wires connected to the given tower. 20' 18 m 50' 2

14 Lesson22.notebook Example: Determine the width of the lake based on the information the surveyor has provided in the diagram. 405 m 80' 325 m Homework: pg. 61, #1 12 pg. 64, #1 13 3

15 Lesson23.notebook Topic: Multi Step Three Dimensional Trigonometric Applications Learning Goal: I can use my understanding of the primary trig ratios, Sine Law and Cosine Law to solve real world problems that require at least 2 steps to solve. Example: Determine the height of the cliff with the given information from the surveyor. 50' 30' 25' 25 m Example: Travis wants to determine the height of a flagpole in the courtyard. He measures the angle of elevation to the top of the pole to be 25' from his current location. he moves 8 m closer to the pole and the new angle of elevation is now 55'. Determine the height of the pole. Homework: pg. 66, #1 10 1

16 Lesson24.notebook Topic: The Ambiguous Case Learning Goal: I can explain why the Ambiguous Case results and I can identify the different cases of the Ambiguous triangle and solve the question accordingly. What is the ambiguous case? The problem arises because our Sine function always wishes to please us! As you know the internal angles of a triangle sum to 180'. When we talked about CAST Rule the following happens... So how do you handle the ambiguous case...? C The three cases: For the given triangle, ΔABC: Case 1: If bsina > a A B Case 2: If bsina = a Case 3: If bsina < a 1

17 Lesson24.notebook Example: Determine the number of solutions for the following triangles. 1) ΔABC where <A = 61', c = 5.1 cm and a = 3.1 cm. 2) ΔABC where <A = 28', c = 3.2 cm and a = 2.4 cm. 3) ΔABC where <A = 47', c = 9.4 cm and a = 3.5 cm. Example: Determine the perimeter for the given belt pulley system. 9 inches 40' 7 inches Homework: pg. 68, #1 10 2