Function periods

How do you find the period of y = tan (3x) )+sin(2.5x)

The answer is 4 according to the questioner but I have no idea why.

Reply 1

tonyiptony

11

Pretty sure the period is not 4. For instance, y=0 when x=0 but y is certainly not 0 when x=4 (by guessing, really).
That said, working out the period of tan(3x) and sin(2.5x) individually should give you some insight as to what to do.
(Also recall what it means for a function to be periodic)

(edited 11 months ago)

Reply 2

old_engineer

11

Original post by maggiehodgson

How do you find the period of y = tan (3x) )+sin(2.5x)

The answer is 4 according to the questioner but I have no idea why.

The period of tan(3x) is pi/3. The period of sin(2.5x) is (2pi)/2.5. You need to find integer values n and m such that n periods of tan(3x) = m periods of sin(2.5x). You could possibly think in terms of lowest common multiple.

Reply 3

maggiehodgson

OP

14

(Original post by old_engineer)The period of tan(3x) is pi/3. The period of sin(2.5x) is (2pi)/2.5. You need to find integer values n and m such that n periods of tan(3x) = m periods of sin(2.5x). You could possibly think in terms of lowest common multiple.

Thanks but I'm still no nearer getting 4.

Reply 4

mqb2766

21

Original post by maggiehodgson

(Original post by old_engineer)The period of tan(3x) is pi/3. The period of sin(2.5x) is (2pi)/2.5. You need to find integer values n and m such that n periods of tan(3x) = m periods of sin(2.5x). You could possibly think in terms of lowest common multiple.

Thanks but I'm still no nearer getting 4.

Are you sure the answer is not 4pi, so a bit over 12 ...
https://www.desmos.com/calculator/9xtse2r73m

Reply 5

maggiehodgson

OP

14

(Original post by mqb2766)Are you sure the answer is not 4pi, so a bit over 12 ...
https://www.desmos.com/calculator/9xtse2r73m

Hi I can't find the question again - it was on a website. I'll keep looking. Thanks for helping all the same.

Reply 6

mqb2766

21

Original post by maggiehodgson

(Original post by mqb2766)Are you sure the answer is not 4pi, so a bit over 12 ...
https://www.desmos.com/calculator/9xtse2r73m

Hi I can't find the question again - it was on a website. I'll keep looking. Thanks for helping all the same.

The answer is 4pi, so just make sure you understand why. As above, itts the lcm of the time periods of each function.

Reply 7

maggiehodgson

OP

14

Original post by mqb2766

The answer is 4pi, so just make sure you understand why. As above, itts the lcm of the time periods of each function.

Yes, thanks. I do understand it now. The answer given really didn't help did it.

Reply 8

mqb2766

21

Original post by maggiehodgson

Yes, thanks. I do understand it now. The answer given really didn't help did it.

With a bit of insight the time period had to be a multiple of pi, but as you say, wrong answers dont help.

Function periods

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