Trigonometric Functions Review

4.1 Radian and Degree Measure

Vocab:

·      Trigonometry: “measurement of triangles”

·      Angle: determined by rotating a ray (half-line) about its endpoint

·      Initial side: starting point of the ray

·      Terminal side: position after rotation

·      Vertex: the endpoint of the ray

·      Standard position: vertex located at origin, one ray is on the positive x-axis

·      Positive angles: generated by counterclockwise rotation

·      Negative angles: clockwise rotation

·      Coterminal: angles that have common terminal side

·      Radian: measure of a central angle Ɵ that intercepts an arc s equal in lenghth to radius of circle

 

·      Complementary angles: 2 angles that add up to 90 degrees

·      Supplementary angles: 2 angles that add up to 180 degrees

* 40+140=180*

Degrees to Radians:	Radians to Degrees:

·      Arc length: Ɵ= s / r

Movie Help:

http://www.youtube.com/watch?v=7xEnSrtlkEE

Online Quiz: http://www.sporcle.com/games/akpgunner/degree_radian_conversion

4.2 Trigonometric Functions: The Unit Circle

Vocab:

·      Unit circle:

Definitions of Trigonometric Functions:

Even and Odd Trigonometric Functions

The cosine and secant functions are even.

Cos (-t)= cos t                    sec (-t) = sec t

The sine, cosecant, tangent, and cotangent functions are odd.

Sin (-t) = -sin t                    csc (-t)= -csc t

Tan (-t) = -tan t                      cot (-t)= -cot t

Movie Help:

http://www.khanacademy.org/math/trigonometry/v/unit-circle-definition-of-trig-functions

4.3 Right Triangle Trigonometry

     Sines, Cosines, and Tangents of Special Angles

Reciporcal and Phythagorean Identities:

Quotient Identities:

Online Quiz:

http://www.purposegames.com/game/937ea535

4.4 Trigonometric Functions of Any Angle

·      Reference angles: the acute angle Ɵ formed by the terminal side of Ɵ and the horizontal axis.  

Movie Help:

http://www.youtube.com/watch?v=Cg70E506maw

Online Quiz:

http://www.mathwarehouse.com/trigonometry/reference-angle/finding-reference-angle.php

4.5 Graphs of Sine and Cosine Functions

·      Parent functions:

y= sin x, y= cos x

amplitude: half the distance between the maximum and minimum values of the function

amplitude= absolute value of a

period: let b be a positive real number.

Movie Help:

http://www.youtube.com/watch?v=8nJjVku-q68

Online Help:

http://www.cliffsnotes.com/study_guide/Graphs-Sine-and-Cosine.topicArticleId-11658,articleId-11595.html

4.6 Graphs of Other Trigonometric Functions

Movie Help:

http://www.youtube.com/watch?v=jpy11Lzi1KQ

Online Help:

http://www.onlinemathlearning.com/reciprocal-function.html

4.8 Applications and Models

Example:

A bug is standing x feet away from the house. Find out how many feet the bug is away from the house?

Online Help:

http://www.algebralab.org/lessons/lesson.aspx?file=Trigonometry_TrigApplications.xml

Movie Help:

http://www.youtube.com/watch?v=-QOEcnuGQwo