1. TRIGONOMTERY
Ms. Carter

2. 2.3 @ FOUNDATION LEVEL
You should be able to..
- solve problems that involve finding heights and distances from
right-angled triangles (2D only)
−
use of the theorem of Pythagoras to solve problems (2D
only)
−
solve problems that involve calculating the cosine, sine and
tangent of angles between 0 and 90

3. 2.3 @ FOUNDATION LEVEL
You should be able to..
- solve problems that involve finding heights and distances from
right-angled triangles (2D only)
−
use of the theorem of Pythagoras to solve problems (2D
only)
−
solve problems that involve calculating the cosine, sine and
tangent of angles between 0 and 90
THIS YOU CAN DO!!!! RIGHT?!

4. AT PASS YOU MUST
be able to...
- use trigonometry to calculate the area of a triangle
−
use the sine and cosine rules to solve problems (2D)
− define sin θ and cos θ for all values of θ
−
define tan θ
−
calculate the area of a sector of a circle and the length of an arc and
solve problems involving these calculations

5. CALCULATE THE AREA OF A
TRIANGLE
You can do this by using the ‘Sine Rule’.
And Or the Area of a Triangle Formula 1/2ab sin C.

6. SINE AND COSINE RULES TO
SOLVE 2D PROBLEMS
Cosine Rule a² = b² + c² - 2bc cos A

7. WHAT DO YOU HAVE TO
DEFINE?
- sin θ and cos θ for
all values of θ
- tan θ

8. LASTLY
calculate the area of a sector of a circle and the length of an arc and
solve problems involving these calculations

9. LASTLY
calculate the area of a sector of a circle and the length of an arc and
solve problems involving these calculations
For the moment that is ALL the Pass Material!
AND
Luckily for you I made you a present during the Snow
Days cause I’m good like that!

10. GRAPHS OF
TRIGONOMTERIC
FUNCTIONS
The Maths LC Syllabus 2010/11 says that:
Students working at LC HL should be
able to
- graph trigonometric functions of
type aSin nx , aCos nx for a, n ∈ N.

11. WHY STUDY THESE GRAPHS?
Most commonly used graphs in statistics and
engineering.
They are used for modelling many different natural
and mechanical phenomena (popultions, acoustics).
You must be able to graph Periodic Graphs. These
are graphs that the shape repeats itselve after a
certain amount of time.
Anything that has a regular cycle(like tides, rotation of
the earth) can be modelled using a sine or cosine
curve.

12. GRAPH OF Y=SINX
The function y = sinx may be graphed like any other function by taking different
values for x and then finding the corresponding y - values.
The table below shows angles between 0º and 360º and the value of
the sine ❨y-value❩ of each of these angles
x= 0º 45º 90º 135º 180º 225º 270º 315º 360º
y = sinx 0 0.7 1 0.7 0 -0.7 -1 -0.7 0

13. If the values of x are extended through another full
rotation of 360º or - 360º, the values of sinx are
repeated for each full rotation of 360º (or 2π)
From this grpah it can be seen that
the values of sine x repeat themselves
every 360º.
The highest y-value of the graph is 1
and the lowest is -1.
Thus the range of the function is
[-1,1]

14. USING THE SAME METHOD
GRAPH Y=COSX IN THE
DOMAIN -180º≤X≤540º
What do you notice about this graph?

15. I NOTICE..
It’s a periodic graph with a period of 360º.
The range is also [-1,1].

16. OFF YOU GO AND TRY
Y=TANX
Whats different about this graph?

17. I THINK IT’S..
It repeats itself every 180º or pi.
O! and there are two vertical asymptotes at x = 90º
and at x = 270º.

18. GRAPHS OF TAN X
There are uncommon but they do occur in
engineering and science problems.
Remember that tan x = sinx/cosx and for some
values of x cosx has value 0.
For example x = π/2 and x = 3π/2.
When this happens we have 0 in the denominator of the
fraction and this means it is undefined.
So there will be a gap in the curve and this gap is called a
discontinuity.

19. IN ACTION
http://www.intmath.com/trigonometric-graphs/4-
graphs-tangent-cotangent-secant-cosecant.php

20. LETS INTERPRET
y = tan x

30. INTERPRETING GRAPHS