Trigonometry
ACT Review
Definition of Trigonometry
It is a relationship between the angles
and sides of a triangle.
Radians
(x,y) = (Rcos (θ) , Rsin (θ) )
( 1 cos (30˚) , 1 sin (30 ˚) =
The radian is a unit of plane angle, equal to 180/π (or 360/(2π)) degrees
Unit Circle Video:
http://www.youtube.com/watch?v=ao4EJzNWmK8&feature=relmfu
Degrees to Radians Conversion
To convert degrees into radians, multiply the degree by ∏/180˚
To convert radians into degrees, multiply the radian by 180˚/ ∏
Radian-Degree
Conversion:
http://www.youtub
e.com/watch?v=c
LBKOYmHuDM&N
R=1
Conversion Examples
Example 1: Convert 60˚ into radians
Example 2: Convert ∏/4 into degrees
∏/4* (180˚/ ∏)=45 ˚
You Should Know:
Trigonometry Basics
Opposite Side: The side
opposite to the angle (θ)
Adjacent Side: The side
adjacent to the angle (θ)
Hypotenuse: The side
opposite to the 90˚ angle,
which is also the longest
side of the triangle
Starting with Sine & Cosine
Trigonometry Basics (cont’d.)
A useful anagram to
help you remember
the formulas is SOH
CAH TOA.
For example, SOH
corresponds to sin
of angle is equal to
opposite over
hypotenuse.
Example – Basic Relationships
Sin (A) = Opposite/Hypotenuse
= 12/13
Cos (A) = Adjacent/Hypotenuse
= 5/13
Tan (A) = Opposite/Adjacent
= 12/5
Csc (A) = Hypotenuse/ Opposite
= 13/12
Sec (A) = Hypotenuse/ Adjacent
= 13/5
Cot (A) = Adjacent/ Opposite
= 5/12
Reciprocal Identities
Csc(θ) is the
reciprocal of sin(θ)
sec(θ) is the
reciprocal of cos(θ)
cot(θ) is the
reciprocal of tan(θ)
Trigonometry Basics (cont’d.)
If you take the the sin,tan,csc or
cot of -θ, then it is the same thing
as taking the sin,tan,csc or cot of
θ and multiplying it by -1.
The cos and sec of –θ is the
same as cos and sec of θ.
If you add a multiple of 2∏ to an
angle and determine the value
of sin and cos, then the answer
will be the same.
(Example: sin(5∏)=sin(5 ∏+2
∏)
Trigonometry Basics (cont’d.)
Inverse Function Example
Thus, y = n/4 or y = 45°
Law of sines, cosines, and tangents
Law of Sines Example
Identity Formulas
Half Angle Example
Example: Find the value of sin 15° using the sine half-angle
relationship.
Sum and Difference Example
Product to Sum Example
Just like the other identity formulas, cofunction and double angle formulas are
mainly used to simplify expressions so that an exact value may be reached.
References
[1] http://tutorial.math.lamar.edu/pdf/Trig_Cheat_Sheet.pdf
[2] http://www.intmath.com/Analytic-trigonometry/4_Half-angle-formulas.php
[3] http://www.sosmath.com/trig/prodform/prodform.html
[4] http://www.analyzemath.com/Trigonometry_2/Use_sum_diff_form.html
[5] http://www.intmath.com/Analytic-trigonometry/4_Half-angle-formulas.php
[6]http://www.tutorvista.com/content/math/trigonometry/trigonometry/mathtrigonometry.php
[7] http://www.nipissingu.ca/calculus/tutorials/trigonometry.html
[8]http://www.algebralab.org/lessons/lesson.aspx?file=Trigonometry_TrigLawSi
nes.xml
[9] http://www.cimt.plymouth.ac.uk/projects/mepres/step-up/sect4/index.htm