Block Five Flashcards
How to solve an simultaneous equation
- times each sun to have at least one term the same number
- if it is the same sign you subtract
- if it is a different sign you add
you then factorise your find one term such as x - substitute the answer in to find the other term
What must you do to get full marks when solving simultaneous equations
you just write a sentence to clarify your answer
you must ensure you write just p and not £0.9p
Pythagoras theroem in right angles triangles
a2 + b2 = c*2
c= the hypotenuse - longest side
how to find the unknown side using pythagoras theroem
a2 + b2 = c2
change the subject
182 = y2 - 92
y2 = 324 - 81
y2 = 243
y= 15.6m
What can pythagoras theroem by used to prove
whether a triangle is right angled or not
How to solve an equation using pythagoras’ theroem
C2 = X
A2 + B* 2 = X
1.32 = 1.69
0.52 + 1.2 *2 = 1.69
so by the converse of pythagoras this is a right angles triangle
What must you write in order to get full marks
you must write
so by the converse of pythagoras this is / is not a right angled triangle
What is an amplitude of the graph
half the distance between the maximum and minimum values of the graph
what is the period of a graph
the distance along the x axis over which the graph completes one full wave
ther period of y = sinx and y = cosx is 360
in the equation y = a Cosx + b
what does a mean
amplitude
in the equation y = a Cosx + b
what does b mean
if the graph has moved up of down
how to identify a cos graph
a cos graph starts at the max amplitude and goes down
how to identify a sin graph
a sin graph starts at zero and goes up to the max value
in the equation y = a Sin ( bx ) + c
what does bx mean
if the period has changed
e.g Y = Sin 2 x
period = 180
what does sin ( x + a ) mean
sin ( x - a ) and cos ( x - a )
is if graph has moved to the right
sin ( x + a ) and cos ( x + a )
is if graph has moved to the left
how to identify a tan graph
the amplitude is infinite
What is the period of a tan graph
y = tanx is 180
Describe what is positive in a cast diagram
x all is positive
180 - x sin is positive
180 + x cos is positive
360 - x tan is positive
solve Sinx = 1/2
x = Sin-1 ( 1/2 )
- using the cast diagram we know that because the fraction is positive we have to look at the two sectors which have a positive value for sin
x = 30 , 180 - 30
x = 30 , 150
solve 5tanx + 2 = 0
- rearrange tanx = - 2/5
this time the fraction is negitive so we have to pick the two sections when tan is negitive
x = 180-60 , 180+60
x = 120 , 240
what does tanx equal
tanx = sinx / cosx
what does 1 equal
sin2x + cos2x = 1
when solving trig indenties
you just make sure the left side matches the right hand side
what are exact values
they can be used to solve trig equations without a calculator
what does SohCahToa stand for
Sin = opp/ hypot
Cos = adj / hypot
Tan = opp / adj
describe the yellow triangle in exact values
hypot = 2
adj = 1
opp = root 3
bottom left angle = 60
top angle = 30
right angle = 90
describe the blue triangle in exact values
opp = 1
adj = 1
hypot= root 2
inside angles = 45
right angle = 90
what do we use SohCahToa for
to find any missing angle or side in a right angled triangle only
how to solve 3D pythagoras
first you must find d by using pythagoras
AD2 = length x bridth
AD = root L x B
then find the other triangle
AB * 2 = root ( LxB) + H
AB = root 90 eg
AB = 3 root 10 cm
What is a chord
a line joins from one side to the other side of a circle is called a chord
What is the biggest chord in a circle
diameter
when is pythagoras theroem used in a circle
Where a right angles triangle can be formed
How do the radius and chord interact
a radius and chord intersect at the right angle
radius divides chord in equal parts
How to calculate the height of a circle
Take away the radius from overall height
use pythagoras theron to find height of triangle and then add or subtract that onto your value
