Math Is Fun Forum

markosheehan

Member

Registered: 2016-06-15

Posts: 51

trigonometric functions

when does sin(x)=sin(-Π/3)    where     x is greater than 0 but less than 4Π.  x stands for theta. i could work out the first place where they cross it is 4Π/3 and i would of said the next place where they cross is 3Π. but the back of the book says it is 5Π/3.  im a bit confused. if you put in 3Π in to both of them they both equal 0. yet this is not one of the answers?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: trigonometric functions

hi markosheehan

if you put in 3Π in to both of them they both equal 0

  Both? There is only one x so how are you doing this?

sin(-pi/3) = minus root 3 over 2.  So you're looking for solutions in the third and fourth quadrant.  4pi/3 is one and its mirror image in the y axis would be 5pi/3.

For questions like these I always sketch axes and mark on a line (from the origin) to indicate one angle eg.  minus pi/3 and then think about where else a line could be to give the same (y) coordinate.

note also: 5pi/3 and -pi/3 give the same line.

and there'll be two more solutions before you get to 4pi.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

markosheehan

Member

Registered: 2016-06-15

Posts: 51

Re: trigonometric functions

sorry i posted the question wrong its when does the sin theta$ graph equal negative root three all over two. i know that the first time the sin graph equals negative root 3 all over 2 is at 4pi/3 but how do you know that it also occurs at 5pi/3. i understand myself that it will equal it again by looking at the sin graph but how do you know it exactly occurs at 5pi/3

Last edited by markosheehan (2016-10-27 08:16:42)

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: trigonometric functions

Last edited by thickhead (2016-10-27 17:26:53)

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(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
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Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: trigonometric functions

hi markosheehan

The sine curve has lots of vertical lines of symmetry:

Here's a sequence in radians going up by 60 degrees each time

pi/3   2pi/3   3pi/3 = pi   4pi/3   5pi/3   6pi/3 = 2pi etc etc.

My first dotted line of symmetry is at 3pi/2 which is exactly half way between 4pi/3 and 5pi/3  [4pi/3 + 5pi/3]/2 = 9pi/6 = 3pi/2

Hope that helps,

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob