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3 years ago

Solve tan x=sin x giving all possible solutions

Mathematics

1 answer:

ZanzabumX [31]3 years ago

3 0

Answer:

x = 2 π n_1 for n_1 element Z

or x = π n_2 for n_2 element Z

Step-by-step explanation:

Solve for x:

tan(x) = sin(x)

Subtract sin(x) from both sides:

tan(x) - sin(x) = 0

Factor sin(x) from the left hand side:

sin(x) (sec(x) - 1) = 0

Split sin(x) (sec(x) - 1) into separate parts with additional assumptions.

Assume cos(x)!=0 from sec(x):

sec(x) - 1 = 0 or sin(x) = 0 for cos(x)!=0

Add 1 to both sides:

sec(x) = 1 or sin(x) = 0 for cos(x)!=0

Take the reciprocal of both sides:

cos(x) = 1 or sin(x) = 0 for cos(x)!=0

Take the inverse cosine of both sides:

x = 2 π n_1 for n_1 element Z

or sin(x) = 0 for cos(x)!=0

Take the inverse sine of both sides:

x = 2 π n_1 for n_1 element Z

or x = π n_2 for cos(x)!=0 and n_2 element Z

The roots x = π n_2 never violate cos(x)!=0, which means this assumption can be omitted:

Answer: x = 2 π n_1 for n_1 element Z

or x = π n_2 for n_2 element Z

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Answer:

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3 years ago

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Express the terms of the following sequence by giving a recursive formula.

emmasim [6.3K]

The recursive formula for given sequence is: $a_n = a_{n-1}-7$

And the terms will be expressed as:

$a_1 = 11\\a_2 = a_{2-1} - 7 \\a_2= a_1 - 7\\a_2 = 11- 7\\a_2 = 4\\a_3 = a_{3-1} - 7 \\a_3= a_2 - 7\\a_3 = 4 - 7\\a_3 = -3\\a_4 = a_{4-1} - 7 \\a_4= a_3 - 7\\ a_4= -3 - 7\\a_4 = -10\\a_5 = a_{5-1} - 7 \\a_5= a_4 - 7\\a_5 = -10 - 7\\a_5 = -17\\$

Step-by-step explanation:

First of all, we have to determine if the given sequence is arithmetic sequence or geometric. For that purpose, we calculate the common difference and common ratio

Given sequence is:

11,4,-3,-10,-17...

Here

$a_1 = 11\\a_2 = 4\\a_3 = -3\\So,\\d = a_2 - a_1 = 4-11 = -7\\d = a_3-a_2 = -3-4 = -7$

As the common difference is same, given sequence is an arithmetic sequence.

A recursive formula is a formula that is used to generate the next term of the sequence using the previous term and common difference

So, the recursive formula for an arithmetic sequence is given by:

$a_n = a_{n-1} +d\\Putting\ d = -7\\a_n = a_{n-1}-7$

Hence,

The recursive formula for given sequence is: $a_n = a_{n-1}-7$

And the terms will be expressed as:

Keywords: arithmetic sequence, common difference

Learn more about arithmetic sequence at:

#LearnwithBrainly

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3 years ago

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VikaD [51]

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Source:
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Solve tan x=sin x giving all possible solutions​

Solve tan x=sin x giving all possible solutions