Trig 1 Solutions

# Trig 1 Solutions - x 16 Using the picture from(15 we have...

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Homework 1 Solutions Math 113 Spring 2009 1. Degrees are the portion of the circle multiplied by 360. Radians are deﬁned to be arc length divided by radius. The conversions are 1radian = 180 π 1 = π 180 radians 2. Radians are a scaled distance. They are distance divided by radius. 3. θ = 3 / 5 4. A) 2 π/ 3 B) - 11 π/ 3 C) 4 π/ 3 D) 24 π E) π 2 / 180 F) 6 π 2 5. A) 540 B) 270 C) 420 D) 64800 π E) - 495 F) 12000 6. 180 / 17 π radians 7. 2 30 π units 8. 3 / 8(1 . 2 kg) = . 45 kg 9. r = 2 10. 2400 / 17 π radians 11. 1 2 (34) 2 ± 7 π 12 ² - 1 2 (18) 2 ± 7 π 12 ² 12. 105 π/ 2 m 13. sin x is the length of the opposite side divided by the length of the hypotenuse. 14. cos x is the length of the adjacent side divided by the length of the hy- potenuse. 15. On the circle, draw a triangle for x and one for - x . Label the hypotenuse c , the adjacent side a and the opposite side b and - b , respectively. Then sin( - x ) = - b c = - sin

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Unformatted text preview: x 16. Using the picture from (15), we have cos(-x ) = a c = cos x 1 2 17. a 2 + b 2 = c 2 a 2 c 2 + b 2 c 2 = 1 ± a c ² 2 + ³ b c ´ 2 = 1 cos 2 x + sin 2 x = 1 18. Quadrants II and IV because tangent is sine divided by cosine and so one of the two must be negative and the other positive. 19. cos θ = 4 / 5 and tan θ = 3 / 4 20. cos θ =-4 / 5 and tan θ =-3 / 4 21. Sine is opposite over hypotenuse and the hypotenuse is always the longest side. Hence, sine can never be larger than 1. 22. ± 4 / 5 23. Because adding a complete rotation around the circle produces the same terminal side and hence the same triangle and hence the same values of the trig functions. 24. There are four. 25. sin θ = 3 / 5 and cos θ =-4 / 5...
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Trig 1 Solutions - x 16 Using the picture from(15 we have...

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