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3 years ago

What is the amplitude of the cosine function corresponding to the secant function graphed below ? a. -2 b. -1 c. 2 d. 3

Mathematics

1 answer:

Bas_tet [7]3 years ago

7 0

Answer:

Step-by-step explanation:

From the graph, we obtain the trigonometric function as:

$y=2 \sec x+1$

The corresponding cosine function have equation.

$y=2\cos x+ 1$

This function is of the form: $y=a\cos bx+c$

where $|a|$ is the amplitude.

Therefore the amplitude is |2|=2

The third choice is correct

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Read 2 more answers

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otez555 [7]

<h3>Answer: 31</h3>

=======================================

Work Shown:

Use the value of a0 to find the value of a1. The idea is you double the previous value, and then add 1.

$a_{n+1} = 2*(a_n) + 1\\\\a_{0+1} = 2*(a_0) + 1\\\\a_{1} = 2*(1) + 1\\\\a_{1} = 3\\\\$

Which is then used to find the value of a2. Follow the same process as before (double the previous value and then add 1).

$a_{n+1} = 2*(a_n) + 1\\\\a_{1+1} = 2*(a_1) + 1\\\\a_{2} = 2*(3) + 1\\\\a_{2} = 7\\\\$

This is used to find a3

$a_{n+1} = 2*(a_n) + 1\\\\a_{2+1} = 2*(a_2) + 1\\\\a_{3} = 2*(7) + 1\\\\a_{3} = 15\\\\$

Finally we can now find a4

$a_{n+1} = 2*(a_n) + 1\\\\a_{3+1} = 2*(a_3) + 1\\\\a_{4} = 2*(15) + 1\\\\a_{4} = 31\\\\$

Recursive sequences like this aren't too bad if n is small, but as n gets larger, things become more tedious. For those cases, its best to try to find a closed form equation. If not, then the next best thing is using a spreadsheet to automate the process.

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