Integration P1

Question 1

what is the integration of sinx

Answer 1

-cosx + c

Question 2

what is the integration of cosx

Answer 2

sinx + c

Question 3

what is the integration of 1/x

Answer 3

ln|x| + c

Question 4

what is the integration of 1 / (ax + b)

Answer 4

1/a ln(ax + b) + c where (ax + b) is +ve

Question 5

what is the integration of sin(ax + b)

Answer 5

-1/a cos(ax + b) + c

Question 6

what is the integration of cos(ax + b)

Answer 6

1/a sin(ax + b) + c

Question 7

what is the inverse of sin x

Answer 7

1 / cosec x

Question 8

what is the inverse of cos x

Answer 8

1 / sec x

Question 9

what is the inverse of tan x

Answer 9

1 / cot x

Question 10

what does sin^2x + cos^2x =

Answer 10

1

Question 11

what does sec^2x =

Answer 11

tan^2x + 1

Question 12

what does 1 + cot^2x =

Answer 12

cosec^2x

Question 13

what are the three C’s on the right side of the magic hexagon from top to bottom

Answer 13

• cos
• cot
• cosec

Question 14

what are the three remaining functions on the left side of the hexagon, from top to bottom

Answer 14

• sin
• tan
• sec

Question 15

what is the rule for working out the quotient identities

Answer 15

• going either clockwise or anti clockwise

- the identity you start off with = the next identity next to it divided by the identity next to that one

Question 16

using the quotient rule, what are the two identities for cot

Answer 16

• cot = cos / sin

- cot = cosec / sec

Question 17

what is the first rule for working out the product identities

Answer 17

• a function between any two functions

- is equal to those two functions multiplied together

Question 18

using that first rule what is the product of tan and cos

Answer 18

tan cos = sin

Question 19

what is in the middle of the hexagon

Answer 19

the number 1

Question 20

what is the second rule for working out the product identities

Answer 20

• for two functions opposite each other

- their product is equal to 1

Question 21

what is the value tan cot

Answer 21

tan cot = 1

Question 22

what is the rule for working out reciprocal identities

Answer 22

a function is equal to 1 over the function opposite it

Question 23

what is the reciprocal identity for cot

Answer 23

cot = 1 / tan

Question 24

what is the rule for working out co-function identities

Answer 24

• by going horizontally across the hexagon in either way
• with a function = f(x) where x is an angle in degrees
• the function f(x) equals the function across it with g(90 - x)

Question 25

using this rule, what does sinx equal

Answer 25

sinx = cos(90-x)

Question 26

what does cosecx equal

Answer 26

cosecx = sec(90-x)

Question 27

what is the first rule for working out the Pythagorean identities

Answer 27

• going clockwise/anticlockwise around the three inside triangles
• starting at the top, across, then ending at the bottom gives you an addition identity
• where the square of the first two functions equals the square of the last one

Question 28

using this rule, what does tan^2x + 1 equal

Answer 28

tan^2x + 1 = sec^2x

Question 29

what is the second rule for working out the pythagorean identities

Answer 29

• going clockwise/anticlockwise around the three inside triangles
• starting at the bottom, going up, then across gives you a subtraction identity
• where the square of the first two functions equals the square of the last one

Question 30

using this rule what does 1 - cos^2x equal

Answer 30

1 - cos^2x = sin^2x