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Assignment 5: Negative Angle Identities - Plane Trigonometry | MATH 111, Assignments of Trigonometry

University of Arizona (UA)Trigonometry

Material Type: Assignment; Class: Plane Trigonometry; Subject: Mathematics Main; University: University of Arizona; Term: Unknown 1989;

Typology: Assignments

Pre 2010

Uploaded on 08/26/2009

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Math 111, Supplemental Assignment #5 (Negative Angle Identities)
Set your calculator in radian mode. Round answers to 2 decimal places.
Part I: The negative angle identity for the cosine function
Plot all points on the set of coordinate axes below. Each (x,y) point comes from an
equation cos x = y.
Find cos 0 = _____, cos .2 = _____, cos (-.2) = _____. Plot all three of these points.
Find cos .6 = _____ and cos (-.6) = _____. Plot these two points.
Find cos 1 = _____ and cos (-1) = _____. Plot these two points.
Find cos
2
= _____ and cos
2
= _____. Plot these two points.
Find cos 2 = _____ and cos (-2) = _____. Plot these two points.
If cos 3 = n, then what is cos (-3)?
How are cos 3 and cos (-3) related? (Write an equation.)
For any number x, ifcos x = m, what is cos (-x)?
Write an equation relating cos x and cos (-x). This is the negative angle identity for the
cosine function.
On your calculator graph Y1 = cos (x) and Y2 = cos(-x). How many graphs do you see?
What does this suggest about the relationship between cos x and cos (-x)?
Consider the single graph y = cos x. The graph has what type of symmetry? Such graphs
represent even functions.
pf2

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Math 111, Supplemental Assignment #5 (Negative Angle Identities) Set your calculator in radian mode. Round answers to 2 decimal places. Part I: The negative angle identity for the cosine function Plot all points on the set of coordinate axes below. Each (x,y) point comes from an equation cos x = y. Find cos 0 = _____, cos .2 = _____, cos (-.2) = _____. Plot all three of these points. Find cos .6 = _____ and cos (-.6) = _____. Plot these two points. Find cos 1 = _____ and cos (-1) = _____. Plot these two points. Find cos       2  = _____ and cos        2  = _____. Plot these two points. Find cos 2 = _____ and cos (-2) = _____. Plot these two points. If cos 3 = n, then what is cos (-3)? How are cos 3 and cos (-3) related? (Write an equation.) For any number x, ifcos x = m, what is cos (-x)? Write an equation relating cos x and cos (-x). This is the negative angle identity for the cosine function. On your calculator graph Y1 = cos (x) and Y2 = cos(-x). How many graphs do you see? What does this suggest about the relationship between cos x and cos (-x)? Consider the single graph y = cos x. The graph has what type of symmetry? Such graphs represent even functions.

Part II: Sine function Graph Y1 = sin x and Y2 = sin (-x) on your calculators. How many graphs do you see? Do you think that sin x = sin (-x)? Find sin .2 = _____ and sin (-.2) = _____. How do sin .2 and sin (-.2) relate to each other? (Write an equation.) Find sin .4 = _____. Without using your calculator, make a conjecture (guess) about the value of sin (-.4) = _____. Use your calculator to determine whether your conjecture is correct. For any number x, how do sin x and sin (-x) relate to each other? (Write an equation.) What kind of symmetry does the graph of y = sin x have? Such graphs are called odd functions. Part III: Tangent function We know that tan x = (^) x x cos sin

, provided cos x 0. Write a similar equation for tan (-x) in

terms of sin (-x) and cos (-x). Use negative angle identities for sin (-x) and cos (-x) to rewrite the equation in terms of sin x and cos x. Write the negative angle identity for the tangent function. Recall that nm = n m  (^). tan (-x) = _____ The function y = tan x is what type of function (choose one): odd, even, neither. What type of symmetry does the graph of y = tan x have?