3. integrate mathematical statements into grammatically correct expositions. Assignment: Find all exact solutions to the following equations: 2e 3(3x+5) cos(2³ + 1) = 0 Include a detailed explanation for each mathematical step written in grammatically correct complete sentences within a 2-column format

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 65E
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please help solve this equation. find all the factors of this equation and solve each factor step by step. include an written explanation on how you solved the equation. An example will be given in the second photo attached
sin (7³)
I
x=0
ecos(¹) = 0
= 0
ka, k is an integer
= Vk, k is an integer
=
H=
- Vk, k is an integer
I= Vk, k is an integer
The second equation has no
solution since the exponential
function is positive, implying
that the exponential function
composed with any other func-
tion would also be positive.
We solved the third equation by
first noticing that the sine func-
tion is zero on the unit circle at
the angle locations of 0 and T.
So, all of the angles for which
the sine function is zero would
be exactly the integer multiples
of T. Since the angle is r for the
sine function, we set that equal
to the integer multiples of rand
solved for z by taking the cube
root of both sides of the result-
ing equation.
Next, we combined the solutions
and checked to see if any of them
were extraneous. The domains
of the two sides of the equation
are each (-00, 0o) since the ex-
ponential function, sine and co-
sine functions, and polynomial
functions all have the domain
(-00, 00). So, all of the solu-
tions we found are actual solu-
tions. Now, taking k = 0, we
would have z = V0 = 0, im-
plying that the solution z = 0 is
already included in the solutions
Vk, k is an integer.
I=
This is our final concise answer.
Transcribed Image Text:sin (7³) I x=0 ecos(¹) = 0 = 0 ka, k is an integer = Vk, k is an integer = H= - Vk, k is an integer I= Vk, k is an integer The second equation has no solution since the exponential function is positive, implying that the exponential function composed with any other func- tion would also be positive. We solved the third equation by first noticing that the sine func- tion is zero on the unit circle at the angle locations of 0 and T. So, all of the angles for which the sine function is zero would be exactly the integer multiples of T. Since the angle is r for the sine function, we set that equal to the integer multiples of rand solved for z by taking the cube root of both sides of the result- ing equation. Next, we combined the solutions and checked to see if any of them were extraneous. The domains of the two sides of the equation are each (-00, 0o) since the ex- ponential function, sine and co- sine functions, and polynomial functions all have the domain (-00, 00). So, all of the solu- tions we found are actual solu- tions. Now, taking k = 0, we would have z = V0 = 0, im- plying that the solution z = 0 is already included in the solutions Vk, k is an integer. I= This is our final concise answer.
Show What You Know: Solving Equations with
Various Function Types
MAT 190 Precalculus
Objectives: The purpose of this assignment is for you to:
1. demonstrate your ability to solve equations with various function types;
2. improve your mathematical writing to include full solutions with justifications;
3. integrate mathematical statements into grammatically correct expositions.
Assignment: Find all exact solutions to the following equations:
2e 3(3x+5) cos(x³ + 1) = 0
Include a detailed explanation for each mathematical step written in grammatically correct
complete sentences within a 2-column format.
Transcribed Image Text:Show What You Know: Solving Equations with Various Function Types MAT 190 Precalculus Objectives: The purpose of this assignment is for you to: 1. demonstrate your ability to solve equations with various function types; 2. improve your mathematical writing to include full solutions with justifications; 3. integrate mathematical statements into grammatically correct expositions. Assignment: Find all exact solutions to the following equations: 2e 3(3x+5) cos(x³ + 1) = 0 Include a detailed explanation for each mathematical step written in grammatically correct complete sentences within a 2-column format.
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