Page 286 - Calculus Demystified

Chapter 1

(c) (d) 273

(e) (f)

√
12. (a) sin(8π/3) = sin(2π/3) = 3/2
√ √
(b) tan(−5π/6) =[−1/2]/[− 3/2]= 1/ 3
√
(c) sec(7π/4) = 1/ cos(7π/4) = 2
√ √
(d) csc(13π/4) = csc(5π/4) = 1/ sin(5π/4) = 1/[− 2/2]=− 2
(e) cot(−15π/4) = cot(−7π/4) = cot(π/4) = cos(π/4)/ sin(π/4) =
√ √
[ 2/2]/[ 2/2]= 1
√
(f) cos(−3π/4) =− 2/2
13. We check the first six identities.
√
2
2
2
(a) cos π/3 = 1/2, sin π/3 = 3/2, cos π/3 + sin π/3 =[1/2] +
√
2
[ 3/2] = 1/4 + 3/4 = 1.
√ √
(b) cos π/3 = 1/2, sin π/3 = 3/2, −1 ≤ 1/2 ≤ 1, −1 ≤ 3/2 ≤ 1.
√ √
2
2
(c) tan π/3 = 3, sec π/3 = 2, tan π/3 + 1 =[ 3] + 1 = 3 + 1 =
2
2
2 = sec π/3.
√ √ √
2
2
(d) cot π/3 = 1/ 3, csc π/3 = 2/ 3, cot π/3+1 =[1/ 3] +1 =
√
2
2
4/3 =[2/ 3] = csc π/3.