HOME COURSES PREVIEW REVIEW ABOUT CONTACT
 Toll-Free Info & Ordering M-F: 9am-5pm (PST): (877) RAPID-10
 QUICK TOUR
 Rapid Courses Catalog Mathematics in 24 Hours Chemistry in 24 Hours Biology in 24 Hours Physics in 24 Hours
Math Survival Weekly
Get the insider's tips and tricks in how to survive your math course and ace the next test. Subscribe the Web's only math weekly newsletter for students and learn:
- How to Study Math Effectively
- How to Take Math Courses Strategically
- How to Solve Math Problems Systematically
- How to Score High in Math Exams
- How to Master Math Rapidly

Enter your name and email below and get started today!
 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     - Statistics At-A-Glance     - 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.

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:

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
• 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
Would you like to study the entire math course in 24 hours? Master all important concepts and learn how to solve problems. Super review your upcoming exams with our cheat sheets. Get started with out rapid courses now!
Calculus
Introductory Statistics

To quickly learn about our math rapid learning system, view the movie:
 ©2014 Rapid Learning Center. Privacy Policy | Disclaimer Chemistry Survival Publishing, Biology Survival Publishing and Physics Survival Publishing are the divisions of Rapid Learning Inc.