pre knowledge

Question 1

values of cosx for 0, π, π/2, π/3, π/4 and π/6

Answer 1

1, -1, 0, 1/2, 1/√2, √3 /2

Question 2

values of sinx for 0, π, π/2, π/3, π/4 and π/6

Answer 2

0, 0, 1, √3 /2, 1/√2, 1/2

Question 3

values of tanx for 0, π, π/2, π/3, π/4 and π/6

Answer 3

0, 0, not defined, √3, 1, 1/√3

Question 4

derivative of tanx

Answer 4

sec^2 x

Question 5

derivative of ln(cosx)

Answer 5

-tanx

Question 6

derivative of inverse sinx

Answer 6

1/√(1-x^2)

Question 7

derivative of inverse cosx

Answer 7

• 1/√(1-x^2)

Question 8

derivative of inverse tanx

Answer 8

1/(1+x^2)

Question 9

derivative of inverse sinhx

Answer 9

1/√(1+x^2)

Question 10

derivative of inverse coshx

Answer 10

1/√(x^2 - 1)

Question 11

derivative of inverse tanhx

Answer 11

1/(1-x^2)

Question 12

integration by parts formula

Answer 12

∫f(x)g′(x) dx = f(x)g(x) − ∫g(x)f′(x)dx

Question 13

partial fractions forms

Answer 13

look at notes

Question 14

what is (e^x)(e^y)

Answer 14

e^(x+y)

Question 15

e^x / e^y

Answer 15

e^(x-y)

Question 16

(e^x)^y

Answer 16

e^xy

Question 17

log rules

Answer 17

ln(xy) = ln x + ln y
ln(x/y)= ln x − ln y
ln(x^a) = aln x

Question 18

trig fomulas

Answer 18

cos^2 A + sin^2 A = 1
1 + tan^2 A = sec^2 A

Question 19

hyperbolic trig formulas

Answer 19

cosh^2 A - sinh^2 A = 1
1 - tanh^2 A = sech^2 A

Question 20

double angle formula for trig

Answer 20

sin(2A) = 2 sin A cos A
cos(2A) = cos^2 A − sin^2 A = 2 cos^2 A − 1
tan 2A =2 tan A / 1 − tan^2 A

Question 21

double angle formula for hyperbolic trig

Answer 21

sinh(2A) = 2 sinhA coshA

cosh(2A) = cosh^2 A + sinh^2 A = 2 cosh^2 A − 1

tanh2A =2 tanh A / 1 + tanh^2 A

Question 22

addition formulas for trig

Answer 22

sin(A ± B) = sin A cos B ± cos A sin B

cos(A ± B) = cos A cos B ∓ sin A sin B