Download presentation

Presentation is loading. Please wait.

Published byHamza Drey Modified over 9 years ago

1
**Trigonometry--The study of the properties of triangles**

Trigonometry--The study of the properties of triangles. Trigonometry means angle measurement. Trigonometric Ratio--The ratios of the measures of two sides of a right triangle. Vocabulary

2
Concept

3
**Find Sine, Cosine, and Tangent Ratios**

A. Express sin L as a fraction and as a decimal to the nearest hundredth. Answer: Example 1

4
**Find Sine, Cosine, and Tangent Ratios**

B. Express cos L as a fraction and as a decimal to the nearest hundredth. Answer: Example 1

5
**Find Sine, Cosine, and Tangent Ratios**

C. Express tan L as a fraction and as a decimal to the nearest hundredth. Answer: Example 1

6
**Find Sine, Cosine, and Tangent Ratios**

D. Express sin N as a fraction and as a decimal to the nearest hundredth. Answer: Example 1

7
**Find Sine, Cosine, and Tangent Ratios**

E. Express cos N as a fraction and as a decimal to the nearest hundredth. Answer: Example 1

8
**Find Sine, Cosine, and Tangent Ratios**

F. Express tan N as a fraction and as a decimal to the nearest hundredth. Answer: Example 1

9
A. Find sin A. A. B. C. D. A B C D Example 1

10
B. Find cos A. A. B. C. D. A B C D Example 1

11
C. Find tan A. A. B. C. D. A B C D Example 1

12
D. Find sin B. A. B. C. D. A B C D Example 1

13
E. Find cos B. A. B. C. D. A B C D Example 1

14
F. Find tan B. A. B. C. D. A B C D Example 1

15
**The side adjacent to the 60° angle has a measure of x.**

Use Special Right Triangles to Find Trigonometric Ratios Use a special right triangle to express the cosine of 60° as a fraction and as a decimal to the nearest hundredth. Draw and label the side lengths of a 30°-60°-90° right triangle, with x as the length of the shorter leg and 2x as the length of the hypotenuse. The side adjacent to the 60° angle has a measure of x. Example 2

16
**Definition of cosine ratio**

Use Special Right Triangles to Find Trigonometric Ratios Definition of cosine ratio Substitution Simplify. Example 2

17
Use a special right triangle to express the tangent of 60° as a fraction and as a decimal to the nearest hundredth. A. B. C. D. A B C D Example 2

18
**Estimate Measures Using Trigonometry**

EXERCISING A fitness trainer sets the incline on a treadmill to 7°. The walking surface is 5 feet long. Approximately how many inches did the trainer raise the end of the treadmill from the floor? Let y be the height of the treadmill from the floor in inches. The length of the treadmill is 5 feet, or 60 inches. Example 3

19
**Use a calculator to find y.**

Estimate Measures Using Trigonometry Multiply each side by 60. Use a calculator to find y. KEYSTROKES: ENTER SIN Answer: The treadmill is about 7.3 inches high. Example 3

20
CONSTRUCTION The bottom of a handicap ramp is 15 feet from the entrance of a building. If the angle of the ramp is about 4.8°, about how high does the ramp rise off the ground to the nearest inch? A. 1 in. B. 11 in. C. 16 in. D. 15 in. A B C D Example 3

21
Concept

22
**Use a calculator to find the measure of P to the nearest tenth.**

Find Angle Measures Using Inverse Trigonometric Ratios Use a calculator to find the measure of P to the nearest tenth. Example 4

23
**Answer: So, the measure of P is approximately 46.8°.**

Find Angle Measures Using Inverse Trigonometric Ratios The measures given are those of the leg adjacent to P and the hypotenuse, so write the equation using the cosine ratio. KEYSTROKES: [COS] 2nd ( ÷ ) ENTER Answer: So, the measure of P is approximately 46.8°. Example 4

24
**Use a calculator to find the measure of D to the nearest tenth.**

B. 48.3° C. 55.4° D. 57.2° A B C D Example 4

25
Solve a Right Triangle Solve the right triangle. Round side measures to the nearest hundredth and angle measures to the nearest degree. Example 5

26
**Step 1 Find mA by using a tangent ratio.**

Solve a Right Triangle Step 1 Find mA by using a tangent ratio. Definition of inverse tangent ≈ mA Use a calculator. So, the measure of A is about 30. Example 5

27
**Step 2 Find mB using complementary angles.**

Solve a Right Triangle Step 2 Find mB using complementary angles. mA + mB = 90 Definition of complementary angles 30 + mB ≈ 90 mA ≈ 30 mB ≈ 60 Subtract 30 from each side. So, the measure of B is about 60. Example 5

28
**Step 3 Find AB by using the Pythagorean Theorem.**

Solve a Right Triangle Step 3 Find AB by using the Pythagorean Theorem. (AC)2 + (BC)2 = (AB)2 Pythagorean Theorem = (AB)2 Substitution 65 = (AB)2 Simplify. Take the positive square root of each side. 8.06 ≈ AB Use a calculator. Example 5

29
**So, the measure of AB is about 8.06.**

Solve a Right Triangle So, the measure of AB is about 8.06. Answer: mA ≈ 30, mB ≈ 60, AB ≈ 8.06 Example 5

30
**Solve the right triangle**

Solve the right triangle. Round side measures to the nearest tenth and angle measures to the nearest degree. A. mA = 36°, mB = 54°, AB = 13.6 B. mA = 54°, mB = 36°, AB = 13.6 C. mA = 36°, mB = 54°, AB = 16.3 D. mA = 54°, mB = 36°, AB = 16.3 A B C D Example 5

31
Summary: If you are given the angle, use sin, cos, and tan If you want to find the angle, use sin-1, cos-1, and tan-1

Similar presentations

© 2024 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google