Trigonometric Identities Worksheet With Answers Page 23
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25–1
KEYSTROKES: COS 2nd [SIN
] 3 ÷ 5 ) ENTER .
13-1 Trigonometric Identities
61. PHYSICS The weight is attached to a spring and suspended from the ceiling. At equilibrium, the weight is located 4
feet above the floor. The weight is pulled down 1 foot and released. Write the equation for the distance d of the
weight above the floor as a function of the time t seconds assuming that the weight returns to its lowest position
every 4 seconds.
SOLUTION:
An equation for the function is
.
At equilibrium, the weight is 4 inches above the floor. Therefore, the vertical shift is k = 4.
The weight is 1 foot closer to the floor at its lowest point, so the amplitude a is 1.
The weight returns to its lowest position every 4 seconds, therefore the period is 4.
There is no horizontal shift.
So,
or
.
Evaluate the sum of each geometric series.
62.
SOLUTION:
There are 5 – 1 + 1 or 5 terms.
Find the sum.
63.
SOLUTION:
There are 7 – 1 + 1 or 7 terms.
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