Question

can you explain, why does sin(x) with constantly increasing x go up and down?

In the unit circle, I can get no more than a maximum of x=1 at which point sin=0

Answer 1

sin is a ratio of the sides of a right triangle of hypotenuse 1

Answer 2

if you consider it as the unit circle; the value attributed to the x in sin(x) as an angle; and the angles keep going round and round and round again

Answer 3

it what we call "periodic"

Answer 4

yes, the angle keeps increasing all the time. so, is it actually like sin(alpha) ? in the unit circle both x and y periodic; however the function sine takes numbers > 1 as well

Answer 5

the sin function does necessarily take "numbers". They take angles defined in numerical terms - degrees or radians.

Answer 6

the angle: 57934 has a sine value of sin(57934)

Answer 7

OH! so, the input x is just coincidentally the same as the x in the unit circle?

Answer 8

the same variable name

Answer 9

yes; if we relate sin to the unit circle; we are measureing angles

if we relate sin to the curve on an xy plane, we are saying x = some angle

Answer 10

think of the x axis as the "angle" axis; and the y axis as the "ratio of sides" axis

Answer 11

if we draw the unit circle centered at the origin of the xy plane, then we can relate sin(angle) with a y value; and cos(angle) with an x value

Answer 12

yes

Answer 13

the angle axis is 90-x in the unit circle right? because, if the y value sin(0) we have max x

Answer 14

the angle is smallest for the triangle when x is largest right?

Answer 15

dont confuse the sin curve with the cos curve