CWA CH 13 FINAL_2_97_22

# CWA CH 13 FINAL_2_97_22 - Chapter 13 THE TRIGONOMETRIC...

This preview shows pages 1–4. Sign up to view the full content.

Chapter 13 THE TRIGONOMETRIC FUNCTIONS 13.1 De…nitions of the Trigonometric Functions 1. 60 ± =60 ³ ¼ 180 ´ = ¼ 3 2. 90 ± =90 ³ ¼ 180 ´ = ¼ 2 3. 150 ± =150 ³ ¼ 180 ´ = 5 ¼ 6 4. 135 ± =135 ³ ¼ 180 ´ = 3 ¼ 4 5. 270 ± =270 ³ ¼ 180 ´ = 3 ¼ 2 6. 320 ± =320 ³ ¼ 180 ´ = 16 ¼ 9 7. 495 ± =495 ³ ¼ 180 ´ = 11 ¼ 4 8. 510 ± =510 ³ ¼ 180 ´ = 17 ¼ 6 9. 5 ¼ 4 = 5 ¼ 4 μ 180 ± ¼ =225 ± 10. 2 ¼ 3 = 2 ¼ 3 μ 180 ± ¼ =120 ± 11. ¡ 13 ¼ 6 = ¡ 13 ¼ 6 μ 180 ± ¼ = ¡ 390 ± 12. ¡ ¼ 4 = ¡ ¼ 4 μ 180 ± ¼ = ¡ 45 ± 13. 8 ¼ 5 = 8 ¼ 5 μ 180 ± ¼ =288 ± 14. 5 ¼ 9 = 5 ¼ 9 μ 180 ± ¼ =100 ± 15. 7 ¼ 12 = 7 ¼ 12 μ 180 ± ¼ =105 ± 16. 5 ¼ =5 ¼ μ 180 ± ¼ =900 ± 17. Let ® = the angle with terminal side through ( ¡ 3 ; 4) : Then x = ¡ 3 ;y =4 ; and r = p x 2 + y 2 = p ( ¡ 3) 2 +(4) 2 = p 25 = 5 : sin ® = y r = 4 5 cot ® = x y = ¡ 3 4 cos ® = x r = ¡ 3 5 sec ® = r x = ¡ 5 3 tan ® = y x = ¡ 4 3 csc ® = r y = 5 4 18. Let ® = the angle with terminal side through ( ¡ 12 ; ¡ 5) : Then x = ¡ 12 = ¡ 5 ; and r = p x 2 + y 2 = p 144 + 25 = p 169 = 13 : sin ® = y r = ¡ 5 13 cot ® = x y = 12 5 cos ® = x r = ¡ 12 13 sec ® = r x = ¡ 13 12 tan ® = y x = 5 12 csc ® = r y = ¡ 13 5 19. Let ® = the angle with terminal side through (7 ; ¡ 24) : Then x =7 = ¡ 24 ; and r = p x 2 + y 2 = p 49 + 576 = p 625 = 25 : sin ® = y r = ¡ 24 25 cot ® = x y = ¡ 7 24 cos ® = x r = 7 25 sec ® = r x = 25 7 tan ® = y x = ¡ 24 7 csc ® = r y = ¡ 25 24 20. Let ® = the angle with terminal side through (20 ; 15) : Then x =20 =15 ; and r = p x 2 + y 2 = p 400 + 225 = p 625 = 25 : sin ® = y r = 3 5 cot ® = x y = 4 3 cos ® = x r = 4 5 sec ® = r x = 5 4 tan ® = y x = 3 4 csc ® = r y = 5 3 853

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
854 Chapter 13 THE TRIGONOMETRIC FUNCTIONS 21. In quadrant I, all six trigonometric functions are positive, so their sign is +. 22. In quadrant II, x< 0 and y> 0 : Furthermore, r> 0 : sin μ = y r > 0 ; so the sign is +. cos μ = x r < 0 ; so the sign is ¡ : tan μ = y x < 0 ; so the sign is ¡ : cot μ = x y < 0 ; so the sign is ¡ : sec μ = r x < 0 ; so the sign is ¡ : csc μ = r y > 0 ; so the sing is +. 23. In quadrant III, 0 and y< 0 : Furthermore, 0 : sin μ = y r < 0 ; so the sign is ¡ : cos μ = x r < 0 ; so the sign is ¡ : tan μ = y x > 0 ; so the sign is +. cot μ = x y > 0 ; so the sign is +. sec μ = r x < 0 ; so the sign is ¡ : csc μ = r y < 0 ; so the sign is ¡ : 24. In quadrant IV, x> 0 and 0 : Also, 0 : sin μ = y r < 0 ; so the sign is ¡ . cos μ = x r > 0 ; so the sign is + : tan μ = y x < 0 ; so the sign is ¡ : cot μ = x y < 0 ; so the sign is ¡ : sec μ = r x > 0 ; so the sign is + : csc μ = r y < 0 ; so the sign is ¡ . 25. When an angle μ of 30 ± is drawn in standard po- sition, one choice of a point on its terminal side is ( x;y )=( p 3 ; 1) : Then r = p x 2 + y 2 = p 3+1=2 : tan μ = y x = 1 p 3 = p 3 3 cot μ = x y = p 3 csc μ = r y =2 26. When an angle μ of 45 ± is drawn in standard po- sition, ( )=(1 ; 1) is one point on its terminal side. Then r = p 1+1= p 2 : sin μ = y r = 1 p 2 = p 2 2 cos μ = x r = 1 p 2 = p 2 2 sec μ = r x = p 2 csc μ = r y = p 2 27. When an angle μ of 60 ± is drawn in standard po- sition, one choice of a point on its terminal side is ( ; p 3) : Then r = p x 2 + y 2 = p 1+3=2 : sin μ = y r = p 3 2 cot μ = x y = 1 p 3 = p 3 3 csc μ = r y = 2 p 3 = 2 p 3 3 28. When an angle μ of 120 ± is drawn in standard posi- tion, ( ¡ 1 ; p 3) is one point on its terminal side. Then r = p : cos μ = x r = ¡ 1 2 cot μ = x y = ¡ 1 p 3 = ¡ p 3 3 sec μ = r x = ¡ 2
Section 13.1 De…nitions of the Trigonometric Functions 855 29. When an angle μ of 135 ± is drawn in standard

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 10/07/2010 for the course CALC 2302 taught by Professor Yuly during the Fall '08 term at University of Texas at Dallas, Richardson.

### Page1 / 40

CWA CH 13 FINAL_2_97_22 - Chapter 13 THE TRIGONOMETRIC...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online