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Math Study Lounge
These study sheets are for quick review on the subjects. Refer to our rapid courses for comprehensive review.
    - Getting Started with Algebra
    - Geometry Basics
    - How to Solve Math Problems
    - Trigonometry Quick Review
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    - Calculus Preview
Home » Trigonometry Quick Review

Key Geometry and Trigonometry Terms

  • Degree - unit of angle measurement equal to 1/360 of a circle’s circumference.
  • Radian - unit of angle measurement that is the ratio ofthe circle arc cut off by an angle to the central angle.
  • Sine - on a unit circle, the “y” coordinate for any intersection between a standard angle and the circle.  In a right triangle, the ratio of the length of the opposite side to the length of the hypotenuse.
  • Cosine - on a unit circle, the “x” coordinate for any intersection between a standard angle and the circle.  In a right triangle, the ratio of the length of the adjacent side to the length of the hypotenuse.
  • Tangent - the ratio of sine to cosine or, in a right triangle, the ratio of the length of the opposite side to the length of the adjacent side.
  • Secant - reciprocal of cosine (sec θ = 1 / cos θ).
  • Cosecant - reciprocal of sine (csc θ = 1 / sin θ).
  • Cotangent - reciprocal of tangent (cot θ = 1 / tan θ).
  • General Form of a Trig Function - trig functions take the form y = A f(Bx + C) + D where A, B, C, and D are coefficients that change the characteristics of that trig function.
Degrees and Radians

Common Angles in Both Degrees and Radians

Angle in Degrees

Angle in Radians

0

0

30

∏/6

45

∏/4

60

∏/3

90

∏/2

180

  • Converting Between Degrees and Radians – Set up a ratio using the fact that 180° = ∏ radians: 
    Convert 20° to radians:

Trig Functions and Common Values

Definition for a right triangle
(o=opposite side, a = adjacent side, h = hypotenuse)

Function

Definition

Sine

o/h

Cosine

a/h

Tangent

o/a

Cotangent

a/o

Secant

h/a

Cosecant

h/o

  • Though sine and cosine are related to the unit circle, their practical value comes from being able to solve right triangles:
  • Example:  Given a 40˚ angle and a hypotenuse of 14, find both legs of the right triangle.The proper equation for sine in this case is:
    sin 40˚ = a / 14, so
    14 sin 40˚ = a
    and 9.0 = a
    The proper equation for cosine in this case is:
    cos 40˚ = b / 14, so
    14 cos 40˚ = b
    and 10.7 = b
  • Example:  Leg a is 5 and leg b is 8.  What is the angle that is adjacent to leg b and the hypotenuse?
    The proper equation for tan in this case is:
    tan θ  = 5 / 8, so
    tan θ  = 0.625
    using a table or calculator, we take
    the inverse of tangent:
    θ = 32˚

Common Trig Function Values to be Memorized

Angle in Degrees

Angle in Radians

Sine

Cosine

Tangent

0

0

0

1

0

30

∏/6

1/2

√3/2

√3/3

45

∏/4

√2/2

√2/2

1

60

∏/3

√3/2

1/2

√3

90

∏/2

1

0

Undef.

180

0

-1

0

Graphs of Trig Functions

  • When graphing a trig function either:
    Memorize the graph, domain, range and any asymptotes
    or
    reason out major features of each graph and sketch it accordingly. 

Example of finding a basic graph through reasoning:

  • We know:
    • sin 0° = 0
    • sin 90° = sin π/2 = 1
    • sin 180° = sin π = 0
    • sin 270° = sin 3π/2 = -1
    • sin 360° = sin 2π = 0
  • Additionally:
    • sin π/6 = 1/2
    • sin π/3 = √3/2 = 0.866

 

  • Important traits for y = sin x: 
    • Domain: All real nos.
    • Range: [-1, 1]
    • Repeats every 2π over the entire x axis
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