Question

Trigonometry: Give the domain of the function f(x) = 2 / (x+4) in interval notation.

Answer 1

Totally lost...

Answer 2

@ranga can you help me with this trig? I want to do...

x+4 >= 0
x >= -4

(-4, positive infinite)

Answer 3

This is not a trig question though.

Answer 4

Pre-Calc or Algebra?

Answer 5

Domain of a function is all allowed values of x. Here there is an expression in the denominator and we cannot allow it to go to 0.

so x + 4 cannot be 0. or x cannot be -4. All other values of x are allowed.

So the domain is (-infinity, -4) U (-4, infinity)

where U is the Union symbol.

Note that -4 is an open interval as indicated by the parenthesis ( and ) instead of [ and ].

Yeah, algebra.

Answer 6

Okay, I think this is a trig question but I don't think it really makes since... "Find all values of theta for which sin of theta = 0"

Answer 7

Wouldn't that just equal 0?

Answer 8

The sine function is a periodic function. It repeats the same cycle over and over again both in the positive and the negative direction.

sin(theta) = 0 when theta = 0, pi, 2pi, 3pi .....
as well as -pi, -2pi, -3pi, ....

So theta = n(pi) where n is any integer (...-3, -2, -1, 0, 1, 2, 3, ...)

Answer 9

oh wait.. so it is... 0
since Sin is y/r
at point (1, 0) right?

Answer 10

That is the solution in the first quadrant. If they ask you for a solution in the domain [0, pi/2] then you can stop at theta = 0.
But if they ask a general question with no domain restriction then you will have to say: n*pi where n is any negative, zero or positive integer.

Answer 11

sin(0) = sin(pi) = sin(2pi) = sin(3pi) = sin(-pi) = sin(-2pi) = sin(-3pi) = 0

Answer 12

But Sin can only be 0.. at (1,0) and (-1,0) right?

Answer 13

I am thinking of the quadrants

Answer 14

If they ask in the interval [0, 2pi] when does sin(theta) become zero you can say at theta = 0 and at theta = pi and stop there.

If no domain restriction, then you can rotate theta = 0 by one full rotation and you will end up in the same place, so 0, 0 + 2pi, 0 + 4pi, all are the same angles.

Answer 15

So like added 360 degrees?

Answer 16

adding*

Answer 17

similarly theta = pi, pi + 2pi, pi + 4pi .... will all end up in the same place.
A full 2pi rotation will always end up in the same location.

exactly like adding 360 degrees or 2pi radians.

Answer 18

and you are saying I can add 360 each time but I can also subtract 360 each time as well to go in the opposite correction.

Answer 19

Yes.

Answer 20

Also, once you are out of basic trig where they use angles in degrees in a triangle you have to switch to thinking angle in radians in calculus. So rather than rotating by 360 degrees we will be rotating 2pi radians in calculus.

Answer 21

So I have to remember the Unit Circle?

Answer 22

Not necessary to memorize it. But if you do enough problems you will remember the sin and cos values in the first quadrant for the angles: 0, 30, 45, 60 and 90 degrees or 0, pi/6, pi/4, pi/3 and pi/2 radians and the rest of the angles can be derived just from the first quadrant values.

Answer 23

You can plot the sine curve online that provides a graphing calculator. For example, you can go to: https://www.desmos.com/calculator and type in sin(x) on the left and it will plot it for you. You can then go and click on the points where it crosses the x-axis and it will tell you the x where sin(x) is zero. As you will notice there are infinite number of x values at which sin(x) = 0.

Answer 24

@ranga how did you become so good at Math? Is this a natural talent for you?

Answer 25

IDK. Different people have different things that comes easily to them. I can do a couple of things okay but there are a million things I cannot do that others do very well. I cannot sing, draw or write poetry but it comes easily and naturally to some others.