maths

Question 1

cosh2a =

Answer 1

2cosh(^2)a -1

1 + 2sinh(^2)a

Question 2

tanha 2a =

Answer 2

2tanha / 1 + tanh(^2)a

Question 3

what does 1 equal in hyperbolic functions

Answer 3

cosh(^2)a - sinh(^2)a =1

Question 4

sech(^2)a=

Answer 4

1 - tanh(^2)a

Question 5

-cosech(^2)a =

Answer 5

1- coth(^2)a

Question 6

sinh(x+y) +

Answer 6

sinhxcoshx + sinhycoshx

Question 7

cosh(x+y) =

Answer 7

coshxcoshy + sinhxsinhy

Question 8

what does 1 equal in normal trig

Answer 8

cos(^2)a +sin(^2)a = 1

Question 9

sec(^2)a =

Answer 9

1 +tan(^2)a

Question 10

cosec(^2)a =

Answer 10

1 +cot(^2)a

Question 11

sin2a =

Answer 11

2sinacosa

Question 12

cos2a=

Answer 12

cos(^2)a - sinh(^2)a

2cos(^2)a - 1

1 - 2sin(^2)a

Question 13

tan2a

Answer 13

= 2tana / 1-tan(^2)a

Question 14

compex numbers

2cos(nx) =

Answer 14

z(^n) + 1/z(^n)

Question 15

complex numbers

2isin(nx)

Answer 15

z (^n) - 1/z(^n)

Question 16

y axis reflection

Answer 16

-1 0

0 1

Question 17

x axis reflection

Answer 17

1 0

0 -1

Question 18

y = x reflection

Answer 18

0 1

1 0

Question 19

y = -x reflection

Answer 19

0 -1

-1 0

Question 20

2 d rotation

Answer 20

cosx -sinx

sinx cosx

Question 21

3 x3

x = 0 reflection

Answer 21

-1 0 0
0 1 0
0 0 1

Question 22

y = 0 reflection 3x3

Answer 22

1 0 0
0 -1 0
0 0 1

Question 23

reflection z = 0

Answer 23

1 0 0
0 1 0
0 0 -1

Question 24

rotation about x axis

Answer 24

1 0 0
0 cosx -sinx
0 sinx cosx

Question 25

roation about y axis

Answer 25

cosx 0 -sinx
0 1 0
sinx 0 cosx

Question 26

z axis rotation

Answer 26

cosx -sinx 0
sinx cosx 0
0 0 1

Question 27

What is scalar product

Answer 27

a.b = /a//b/ . cosx

Question 28

what is scalar product if two lines are parallel

Answer 28

a.b = 0

Question 29

angle between 2 lines

Answer 29

cos x = /a.b/ divided by /a//b/

Question 30

angle between line and a plane

Answer 30

sin x = b.n divided by /b//n/

Question 31

angle between 2 planes

Answer 31

modulus of n.n divided by /n//n/

Question 32

how to find intersection of plane and line

Answer 32

1. write equation of line as one single vector
2. subsistutute vector into r.n = d form of plane equation
3. solve to find lamda and then substitute lamda into line equation to get coordinates

Question 33

how to find intersection of two planes along a line

Answer 33

write cartesian from of each equation

eliminate one variable using simultaneous equations and express one variable in terms of the other

substitute the new equation back into original plane equation to get an equation in terms of the original eliminated variable

rewrite the equation found in step 2 and change the subject

then write form of line in cartesian form

Question 34

perpendicular distance between point and a line

Answer 34

find equation for line

find equation from a to b ( a being the point and b being a general point on the line)

AB is perpendicular to line so AB . direction of line = 0
thatll give you lamda

then sub lamda into AB equation and modulus of it is distance

Question 35

distance between point and plane

Answer 35

use formula bok

Question 36

distance between two parralell lines

Answer 36

find BA by doing line 1 - line 2

then set t=lamda - mu

BA is perpendicular to line 1

find t then sub back in and find modulus