SPECIAL

1
Computing the Values of Trig Functions of Acute
Angles
SPECIAL
USING
TRIANGLES
2
The 45-45-90 Triangle
This means I can build a triangle with these
lengths for sides (or any multiple of these
lengths)
We can then find the six trig functions of 45
using this triangle.
45
rationalized
1
45
90
1
Can "flip" these to get other 3 trig functions
3
You are expected to know exact values for trig
functions of 45. You can get them by drawing
the triangle and using sides.
What is the radian equivalent of 45?
You also know all the trig functions for ?/4 then.
45
1
45
90
reciprocal of cos so h over a
1
4
The 30-60-90 Triangle
side opp 60
In a 30-60-90 triangle the sides are in a ratio
of 1- - 2
side opp 90
side opp 30
This means I can build a triangle with these
lengths for sides
We can then find the six trig functions of 30or
60 using this triangle.
30
I used the triangle and did adjacent over
hypotenuse of the 60 to get this but it is the
cofunction of sine so this shows again that
cofunctions of complementary angles are equal.
2
60
90
1
Be sure to locate the angle you want before you
find opposite or adjacent
5
What this means is that if you memorize the
special triangles, then you can find all of the
trig functions of 45, 30, and 60 which are
common ones you need to know.
You also can find the radian equivalents of these
angles.
When directions say "Find the exact value", you
must know these values not a decimal
approximation that your calculator gives you.
6
Using a Calculator to Find Values of Trig
Functions
If we wanted sin 38 we could not use the
previous methods to find it because we don't know
the lengths of sides of a triangle with a 38
angle. We will then use our calculator to
approximate the value.
You can simply use the sin button on the
calculator followed by (38) to find the sin 38
A word to the wise Always make sure your
calculator is in the right mode for the type of
angle you have (degrees or radians)
7
Acknowledgement I wish to thank Shawna Haider
from Salt Lake Community College, Utah USA for
her hard work in creating this PowerPoint. www.sl
cc.edu Shawna has kindly given permission for
this resource to be downloaded from
www.mathxtc.com and for it to be modified to suit
the Western Australian Mathematics Curriculum.
Stephen Corcoran Head of Mathematics St
Stephens School Carramar www.ststephens.wa.edu.
au