Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.4: Multiple-angle Formulas
Problem 72E
Related questions
Question
127, 133 plz
![132. Prove the quotient identities given in identity (3).
131. Prove the reciprocal identities given in identity (2).
136. Challenge Problem If sin (40) = cos (20) and 0 < 46 <
137. Challenge Problem Find the exact value of sin 0 – cos 6
135. Challenge Problem If tan 0 = 3 – sec 0 with 0 in quadran
134. Challenge Problem If 2 sin? 0 + 3 cos 0 = 3 sin 0 cos8 +1
406 CHAPTER 6 Trigonometric Functions
122. Lung Volume Normal resting lung volume V, in mL, for adult
men varies over the breathing cycle and can be approximated
by the model
128. Show that the period of f) = csc 0 is 27
129. Show that the period of f(0) = tan 0 is 7
130. Show that the period of f0) = cot 0 is 7.
[ 27(t - 1.25)
V(t) = 250 sin
+ 2650
5
133. Establish the identity:
where t is the number of seconds after breathing begins. Use
the model to estimate the volume of air in a man's lungs after
2.5 seconds, 10 seconds, and 17 seconds.
(sin 0 cos )2 + (sin 0 sin ø)² + cos? e =1
123. Show that the range of the tangent function is the set of all
real numbers.
with 0 in quadrant I, find the possible values for COS
124. Show that the range of the cotangent function is the set of all
real numbers.
what is sin 0 + cos 0?
125. Show that the period of f(0) = sin 0 is 2r.
[Hint: Assume that 0<p < 2m exists so that
sin (0 + p) = sin 0 for all 0. Let 0 = 0 to find p. Then let
find the exact value of sin ( 80) + cot(40) – 2
to obtain a contradiction.]
cos e - 8 sin 0 = 7 and 180° < 0 < 270°
126. Show that the period of f(6) = cos 0 is 27.
127. Show that the period of f(0) = sec 0 is 27.
Explaining Concepts: Discussion and Writing
138. Write down five properties of the tangent function. Explain
the meaning of each.
139. Describe your understanding of the meaning of a periodic
function.
141. Explain how to find the value of cos (-45°) using even.odi
properties.
142. Explain how to find the value of sin 390° and cos (-45"
using the unit circle.
140. Explain how to find the value of sin 390° using periodic
properties.
Retain Your Knowledge
Problems 143–152 are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your
mind so that you are better prepared for the final exam.
143. Given: f(x) = x² – 3 and g(x) = x - 7, find (fog) (x).
144. Graph f(x) = -2r? + 12r – 13 using transformations. Find the vertex and the axis of symmetry.
145. Solve exactly: e*-4 = 6
146. Find the real zeros of f(x) = x³ - 9x? + 3x – 27.
147. Solve: Vx + 2 - Vx - 5 = 2
148. If the real zeros of g (x) are -2 and 3, what are the real zeros of g(x + 6)?
149. Solve: log4 (x – 5) = 2
K 150. Find c so that f(x) = 6x - 28r + c has a minimum value of
151. Find the intercepts of the graph of -3x + 5y = 15.
A 152. Find the difference quotient for f(x) =
- 5x + 1,
'Are You Prepared?' Answers
1.
2. even
3. False
4. True](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe17a0841-2fee-4282-95e4-cffa14dbd089%2F25309672-1552-4953-b3d8-0c5cb182894f%2Fjcyesi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:132. Prove the quotient identities given in identity (3).
131. Prove the reciprocal identities given in identity (2).
136. Challenge Problem If sin (40) = cos (20) and 0 < 46 <
137. Challenge Problem Find the exact value of sin 0 – cos 6
135. Challenge Problem If tan 0 = 3 – sec 0 with 0 in quadran
134. Challenge Problem If 2 sin? 0 + 3 cos 0 = 3 sin 0 cos8 +1
406 CHAPTER 6 Trigonometric Functions
122. Lung Volume Normal resting lung volume V, in mL, for adult
men varies over the breathing cycle and can be approximated
by the model
128. Show that the period of f) = csc 0 is 27
129. Show that the period of f(0) = tan 0 is 7
130. Show that the period of f0) = cot 0 is 7.
[ 27(t - 1.25)
V(t) = 250 sin
+ 2650
5
133. Establish the identity:
where t is the number of seconds after breathing begins. Use
the model to estimate the volume of air in a man's lungs after
2.5 seconds, 10 seconds, and 17 seconds.
(sin 0 cos )2 + (sin 0 sin ø)² + cos? e =1
123. Show that the range of the tangent function is the set of all
real numbers.
with 0 in quadrant I, find the possible values for COS
124. Show that the range of the cotangent function is the set of all
real numbers.
what is sin 0 + cos 0?
125. Show that the period of f(0) = sin 0 is 2r.
[Hint: Assume that 0<p < 2m exists so that
sin (0 + p) = sin 0 for all 0. Let 0 = 0 to find p. Then let
find the exact value of sin ( 80) + cot(40) – 2
to obtain a contradiction.]
cos e - 8 sin 0 = 7 and 180° < 0 < 270°
126. Show that the period of f(6) = cos 0 is 27.
127. Show that the period of f(0) = sec 0 is 27.
Explaining Concepts: Discussion and Writing
138. Write down five properties of the tangent function. Explain
the meaning of each.
139. Describe your understanding of the meaning of a periodic
function.
141. Explain how to find the value of cos (-45°) using even.odi
properties.
142. Explain how to find the value of sin 390° and cos (-45"
using the unit circle.
140. Explain how to find the value of sin 390° using periodic
properties.
Retain Your Knowledge
Problems 143–152 are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your
mind so that you are better prepared for the final exam.
143. Given: f(x) = x² – 3 and g(x) = x - 7, find (fog) (x).
144. Graph f(x) = -2r? + 12r – 13 using transformations. Find the vertex and the axis of symmetry.
145. Solve exactly: e*-4 = 6
146. Find the real zeros of f(x) = x³ - 9x? + 3x – 27.
147. Solve: Vx + 2 - Vx - 5 = 2
148. If the real zeros of g (x) are -2 and 3, what are the real zeros of g(x + 6)?
149. Solve: log4 (x – 5) = 2
K 150. Find c so that f(x) = 6x - 28r + c has a minimum value of
151. Find the intercepts of the graph of -3x + 5y = 15.
A 152. Find the difference quotient for f(x) =
- 5x + 1,
'Are You Prepared?' Answers
1.
2. even
3. False
4. True
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