Your SlideShare is downloading.
×

×

Saving this for later?
Get the SlideShare app to save on your phone or tablet. Read anywhere, anytime – even offline.

Text the download link to your phone

Standard text messaging rates apply

Like this presentation? Why not share!

- Trigonometry functions of general a... by Jessica Garcia 14904 views
- Trigonometric Function Of Any Angle by guest793408 65013 views
- 5.2.1 trigonometric functions by Northside ISD 3359 views
- Math12 lesson4 by dylanxclusive 2137 views
- Electronic Nicotine Delivery System... by American Legacy F... 2722 views
- Evolving from Ubercart to Drupal Co... by Ryan Szrama 4021 views

7,889

Published on

No Downloads

Total Views

7,889

On Slideshare

0

From Embeds

0

Number of Embeds

0

Shares

0

Downloads

45

Comments

0

Likes

1

No embeds

No notes for slide

- 1. 13-2 Angles of Rotation Holt Algebra 2 Warm Up Lesson Presentation Lesson Quiz
- 2. Draw angles in standard position. Determine the values of the trigonometric functions for an angle in standard position. Objectives
- 3. In Lesson 13-1, you investigated trigonometric functions by using acute angles in right triangles. The trigonometric functions can also be evaluated for other types of angles. An angle is in standard position when its vertex is at the origin and one ray is on the positive x -axis. The initial side of the angle is the ray on the x -axis. The other ray is called the terminal side of the angle.
- 4. Example 3: Finding Reference Angles Find the measure of the reference angle for each given angle. B. = –105° A. = 135° The measure of the reference angle is 45°. The measure of the reference angle is 75°. – 105°
- 5. Check It Out! Example 3 Find the measure of the reference angle for each given angle. The measure of the reference angle is 75° The measure of the reference angle is 65° a. = 105° b. = –115° 105° – 115°
- 6. Check It Out! Example 3 Find the measure of the reference angle for each given angle. The measure of the reference angle is 50° c. = 310° 310°
- 7. To determine the value of the trigonometric functions for an angle θ in standard position, begin by selecting a point P with coordinates ( x, y ) on the terminal side of the angle. The distance r from point P to the origin is given by .
- 8.
- 9. Example 4: Finding Values of Trigonometric Functions P (–6, 9) is a point on the terminal side of in standard position. Find the exact value of the six trigonometric functions for θ . Step 1 Plot point P, and use it to sketch a right triangle and angle θ in standard position. Find r .
- 10. Step 2 Find sin θ , cos θ , and tan θ . Example 4 Continued
- 11. Example 4 Continued Step 3 Use reciprocals to find csc θ , sec θ , and cot θ .
- 12. Because r is a distance, its value is always positive, regardless of the sign of x and y . Helpful Hint
- 13. Check It Out! Example 4 P (–3, 6) is a point on the terminal side of θ in standard position. Find the exact value of the six trigonometric functions for θ . Step 1 Plot point P, and use it to sketch a right triangle and angle θ in standard position. Find r . y x P (–3, 6) θ
- 14. Check It Out! Example 4 Continued Step 2 Find sin θ , cos θ , and tan θ .
- 15. Step 3 Use reciprocals to find csc θ , sec θ , and cot θ . Check It Out! Example 4 Continued
- 16. Lesson Quiz: Part I Draw and angle in standard position with the given measure. 1. 210° 2. –160°
- 17. Find the measure of the reference angle for each given angle. Lesson Quiz: Part II 3 . θ = 290° 4 . θ = –195° 70° 15° 5. P (1, –1) is a point on the terminal side of θ in standard position. Find the exact value of the six trigonometric functions for θ .

Be the first to comment