13 Chapter Review

Connecting BIG ideas and Answering the Essential Questions

1 Modeling You can use combinations of circular functions (sine and cosine) to model natural periodic behavior.	Angles, the Unit Circle, and Radian Measure (Lessons 13-2 and 13-3) One radian is the measure of a central angle of a circle that intercepts an arc of length equal to the radius of the circle.	Translating Sine and Cosine Functions (Lesson 13-7) For the functions y = a sin b ( x − h ) + k , y equals eh sine b open x minus h close plus k comma and y = a cos b ( x − h ) + k , y equals eh cosine b open x minus h close plus k comma | a | absolute value of eh ,  is the amplitude 2 π b fraction 2 pi , over b end fraction  is the period h is the phase shift, or horizontal shift k is the vertical shift
2 Function The graph of y = 4 sin 2 ( x − π 4 ) + 4 y equals 4 sine 2 . open . x minus , pi over 4 . close . plus 4  has amplitude 4, period π, and a minimum at the origin.
3 Function If you know the value of sin θ, find an angle with measure θ in standard position on the unit circle to find values of the other trigonometric functions.	Sine, Cosine, and Tangent Functions (Lessons 13-4, 13-5, and 13-6)	Reciprocal Trigonometric Functions (Lesson 13-8) csc θ = 1 sin θ = 2 sec θ = 1 cos θ = ± 2 3 cot θ = 1 tan θ = ± 3 table with 3 rows and 1 column , row1 column 1 , co-secant theta equals . fraction 1 , over sine theta end fraction . equals 2 , row2 column 1 , secant theta equals . fraction 1 , over cosine theta end fraction . equals plus minus , fraction 2 , over square root of 3 end fraction , row3 column 1 , co-tangent theta equals . fraction 1 , over tangent theta end fraction . equals plus minus square root of 3 , end table

Choose the correct term to complete each sentence.

1. The __?__ of a periodic function is the length of one cycle.
2. Centered at the origin of the coordinate plane, the __?__ has a radius of 1 unit.
3. An asymptote of the __?__ occurs at θ = π 2 , theta equals , pi over 2 . comma  and repeats every π units.
4. A horizontal translation of a periodic function is a(n) __?__.
5. The __?__ is the reciprocal of the cosine function.

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