Exam Trig

Question 1

Sum & Difference Formulas

Answer 1

sin(u+v) = sinu x cosv + cosu x sinv

sin(u-v) = sinu x cosv - cosu x sinv

cos(u+v)= cosu x cosv - sinu x sinv

cos(u-v)= cosu x cosv + sinu x sinv

tan(u+v) = (tanu + tanv)/ (1- tanu x tanv)

tan(uv) = (tanu - tanv)/ (1+ tanu x tanv)

Question 2

Double Angle Formulas

Answer 2

sin2u = 2sinu cosu
cos2u = cos^2u - sin^2u
cos2u = 2cos^2u - 1
cos2u= 1-2sin^2u
tan2u= (2tanu)/ (1-tan^2u)

Question 3

General Identies:

Answer 3

sin^2u + cos^2u = 1
1+tan^2u=sec^2u
1+cot^2u=csc^2u

Question 4

y=tanx

Answer 4

asympotes: π/2, 3π/2, -π/2, -3π/2
range: -infinity, + infinity

period: π
cycle: bx-c= -π/2 & bx-c=π/2

Question 5

y=sinx & cosx

Answer 5

y=k__(bx+c) +d
|k|= amplitude
bx-c= 0
bx-c= 2π
phase shift= c/b
vertical shift= d

Question 6

y=secx

Answer 6

asymptotes: π/2, 3π/2, -π/2, -3π/2
bx-c= -π/2
bx-c= π/2

Question 7

y=cscx

Answer 7

asymptotes:-2π, -π, 0, -π, 2π
bx-c=0
bx-c= π
bx-c = 2π

Question 8

y=cotx

Answer 8

asymptotes:-2π, -π, 0, -π, 2π
bx-c=0
bx-c = 2π

Question 9

y=arcsinx

Answer 9

domain: [-1,1]
range: [-π/2, π/2]

Question 10

y=arccosx

Answer 10

domain: [-1,1]
range: [0, π]

Question 11

y=arctanx

Answer 11

domain: (-infinity, infinity)
range: (-π/2, π/20

Question 12

limit (sinx)/x =
x»0

Answer 12

1

Question 13

limit (1-cosx)/x =
x»0

Answer 13

0