ACTUAL QUESTION: A weight is suspended on a vertical spring. The position x of the weight on the vertical number line is given by the function x= 3 sin (t) + 2 cos (t), where t is time in seconds. a. Find the initial position of the weight (its position at time t= 0). 7* b. Find the exact position of the weight at time t= seconds. a. The initial position of the weight is 2. (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Rationalize all denominators.) b. The exact position of the weight at time t= seconds is O. et3D (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Rationalize all denominators.) A confusing start to an example: A weight is suspended on a vertical spring. The position x of the weight on the vertical number line is given by the function second-S., where t is time in seconds. a. Find the initial position of the weight (its position at time t= 0). b. Find the exact position of the weight at time t= 5 sin (t) + 7 cos (1) seconds. a. To find the initial position of the weight, substitute t = 0 into the given function for x, and evaluate. x= 5 sin (1) + 7 cos (1) =5 sin (0) + 7 cos (0) =5.0+7.1 -7 Replace t with 0. Evaluate sin o and cos 0. Simplify. Thus, the initial position of the weight is Line and Paragraph Spacing 7x 7x b. To find the exact position of the weight at time t=, substitute t= into the given function for x, and evaluate. x= 5 sin (t) +7 cos (t) 7x +7 cos 7x Replace t with =5 sin 7x depending on the quadrant in 7% and cos Evaluate sin 7x lies. Sketch the angle which the terminal side of in standard position.
ACTUAL QUESTION: A weight is suspended on a vertical spring. The position x of the weight on the vertical number line is given by the function x= 3 sin (t) + 2 cos (t), where t is time in seconds. a. Find the initial position of the weight (its position at time t= 0). 7* b. Find the exact position of the weight at time t= seconds. a. The initial position of the weight is 2. (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Rationalize all denominators.) b. The exact position of the weight at time t= seconds is O. et3D (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Rationalize all denominators.) A confusing start to an example: A weight is suspended on a vertical spring. The position x of the weight on the vertical number line is given by the function second-S., where t is time in seconds. a. Find the initial position of the weight (its position at time t= 0). b. Find the exact position of the weight at time t= 5 sin (t) + 7 cos (1) seconds. a. To find the initial position of the weight, substitute t = 0 into the given function for x, and evaluate. x= 5 sin (1) + 7 cos (1) =5 sin (0) + 7 cos (0) =5.0+7.1 -7 Replace t with 0. Evaluate sin o and cos 0. Simplify. Thus, the initial position of the weight is Line and Paragraph Spacing 7x 7x b. To find the exact position of the weight at time t=, substitute t= into the given function for x, and evaluate. x= 5 sin (t) +7 cos (t) 7x +7 cos 7x Replace t with =5 sin 7x depending on the quadrant in 7% and cos Evaluate sin 7x lies. Sketch the angle which the terminal side of in standard position.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.3: The Addition And Subtraction Formulas
Problem 75E
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Hello. I have been trying to understand what this example is trying to tell me. I understand setting the t to zero in the first part, but I cannot figure what numbers to plug in for part 2. How do they get that 7pi/4?? Is that a constant number that I should use to solve all?
Transcribed Image Text:ACTUAL QUESTION:
A weight is suspended on a vertical spring. The position x of the weight on the vertical number line is given by the function x= 3 sin (t) + 2 cos (t), where t is time in seconds.
a. Find the initial position of the weight (its position at time t= 0).
7*
b. Find the exact position of the weight at time t=
seconds.
a. The initial position of the weight is 2.
(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Rationalize all denominators.)
b. The exact position of the weight at time t=
seconds is O.
et3D
(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Rationalize all denominators.)
A confusing start to an example:
A weight is suspended on a vertical spring. The position x of the weight on the vertical number line is given by
the function second-S., where t is time in seconds.
a. Find the initial position of the weight (its position at time t= 0).
b. Find the exact position of the weight at time t= 5 sin (t) + 7 cos (1) seconds.
a. To find the initial position of the weight, substitute t = 0 into the given function for x, and evaluate.
x= 5 sin (1) + 7 cos (1)
=5 sin (0) + 7 cos (0)
=5.0+7.1
-7
Replace t with 0.
Evaluate sin o and cos 0.
Simplify.
Thus, the initial position of the weight is
Line and Paragraph Spacing
7x
7x
b. To find the exact position of the weight at time t=, substitute t= into the given function for x, and
evaluate.
x= 5 sin (t) +7 cos (t)
7x
+7 cos
7x
Replace t with
=5 sin
7x
depending on the quadrant in
7%
and cos
Evaluate sin
7x
lies. Sketch the angle
which the terminal side of
in standard
position.
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