Why does sinx = 0, cosx = 0 and sinx = 1 equal to... (1 Viewer)

[bawd]

Well, I'm confused as to how you solve sinx = 0, cosx = 0 and sinx = 1.

I mean, I know the answers, but don't understand how they are attained. (i.e. sinx = 0, x = 0, 180 and 360 degrees etc) Can somebody please explain in a simple manner how to prove or solve the above equations (don't want to be constantly checking by typing sin180 into calculator etc.) and how you'd read them off a graph? Appreciate the help.

 

[M@ster P]

ok the easiest way to get the answers is to draw the sin and cos graph, and see where they touch at either -1, 0 and 1

 

[bawd]

ok the easiest way to get the answers is to draw the sin and cos graph, and see where they touch at either -1, 0 and 1

What about on a unit circle graph? Besides, don't want to be drawing graphs in exams. (although, I'm pretty sure I'd know by then lol) Just want someone to prove that they are correct, solve from scratch etc.

 

[veloc1ty]

You should be able to figure this out in your head. The sinx and cosx graphs repeat every 180 degrees... so for sinx = 0, you know sinx begins at {0,0} thus the first one is 0. The next one is 0 + 180. The next is 0 + 180 + 180. And so on.

Likewise for cosx = 0, you know cosx begins at {0,1} so the first one must be 90. The next is 90 + 180, and so on.

 

[M@ster P]

well the best way is the graph, and i don't think it would hurt too much to draw one in exams

 

[M@ster P]

You should be able to figure this out in your head. The sinx and cosx graphs repeat every 180 degrees... so for sinx = 0, you know sinx begins at {0,0} thus the first one is 0. The next one is 0 + 180. The next is 0 + 180 + 180. And so on.

Likewise for cosx = 0, you know cosx begins at {0,1} so the first one must be 90. The next is 90 + 180, and so on.

in short the general solutions

 

[Continuum]

Well, I'm confused as to how you solve sinx = 0, cosx = 0 and sinx = 1.

I mean, I know the answers, but don't understand how they are attained. (i.e. sinx = 0, x = 0, 180 and 360 degrees etc) Can somebody please explain in a simple manner how to prove or solve the above equations (don't want to be constantly checking by typing sin180 into calculator etc.) and how you'd read them off a graph? Appreciate the help.

Just draw a unit circle (circle with radius of 1) in your head. You know that cos x is adjacent over hypotenuse but since the radius and thus hypotenuse is 1, cos x would just represent the adjacent side - which is the x-axis. We can thus say that cos x would represent the x-value of a point on the unit circle. The same goes for sin x, it would just represent the opposite side and thus the y-value of a point on the circle.

So when you have sinx=0 for example, you just look at whenever the y-value of a point on the unit circle is 0 - such as 0 and 180 degrees. When you have something like cos x=0, you do it just the same way. When you have the angle being 0 degrees, cos x would be 1 because it represents the x-value so this can't be the answer. When you have the angle being 90 degrees though, you see that the x-value of the point on the unit circle is 0 - thus 90 degrees is a solution to it.

 

[bored of sc]

Just draw a unit circle (circle with radius of 1) in your head. You know that cos x is adjacent over hypotenuse but since the radius and thus hypotenuse is 1, cos x would just represent the adjacent side - which is the x-axis. We can thus say that cos x would represent the x-value of a point on the unit circle. The same goes for sin x, it would just represent the opposite side and thus the y-value of a point on the circle.

So when you have sinx=0 for example, you just look at whenever the y-value of a point on the unit circle is 0 - such as 0 and 180 degrees. When you have something like cos x=0, you do it just the same way. When you have the angle being 0 degrees, cos x would be 1 because it represents the x-value so this can't be the answer. When you have the angle being 90 degrees though, you see that the x-value of the point on the unit circle is 0 - thus 90 degrees is a solution to it.

Are you sure the hypotenuse is 1? I thought it was square root of 2 by pythagoras.

 

[lyounamu]

Are you sure the hypotenuse is 1? I thought it was square root of 2 by pythagoras.

Nah. It's always one because hypotenuse is a "radius" for the circle.

 

[bawd]

Thanks for all the comments. It makes sense now. I remember learning it in Year 10, but not paying attention lol.

 

[me121]

even simpler just remember that sin is y component, cos is x. from those two facts you can work out what you wanted..(in fact they pop up in physics, engineering studies, maths.. all over the place, they will become cemented in your brain because they are so important) no need to worry about drawing the actual circle or worrying about the hypothmuse or anything.

 

[bawd]

even simpler just remember that sin is y component, cos is x. from those two facts you can work out what you wanted..(in fact they pop up in physics, engineering studies, maths.. all over the place, they will become cemented in your brain because they are so important) no need to worry about drawing the actual circle or worrying about the hypothmuse or anything.

Yes, thank you again.