What does sine x do?

Question

I know what sine is: opposite over the hypotenuse. But how does sin work on a graph? I don't see any triangles on the graph. How do you get the values to graph sine?

Answer 1

Sine is a trigonomic function

What it looks like on a graph is a bunch of hills... X represents the angle and Y represents the result of the sine function being applied to the angle

When x=0 for sine(x) (At 0) it is 0 (because sin(0)=0) so it starts at the origin (0,0)

and at sin30=0.5 (because if you know ur special triangles... if the opposite side =1 and hypotenuse =2, you get 1/2, since the angle your corresponding the sides with is 30degrees)

At Sin45=1/rt2 (due to the special triangle when the opposite side =1 and hyp = rt2 and the angle that corresponds to the sides is 45degrees)

At sin60=rt3/2 or... 1.7/2 (due to the opposite side being rt3 and hyp =2)

At sin90=1

This is the highest Y value that the sine graph reaches. It'll then slope down towards 0 in the same pattern I just explained (some of these angles you can calculate in ur head using special triangles like 120, 135, 150). It will reach back down to 0 at 180degrees

Then it will become negative numbers past 180degrees.

Sin210 = -1/2

Sin225 = -1/rt2

Sin240 = -rt3/2

And at Sin270 = -1. Y=-1 is the lowest value that the sine graph reaches

Then the sine graph climbs back up to 0 when x=360 degrees and the hill-pattern cycle continues again.

Wikipedia has a good image of what the sine graph looks like

Answer 2

Imagine a ferris wheel turning, pick one seat on the wheel, let the horizontal axis of the graph be the angle of turn, the vertical be the height above ground.  the seat goes up and down and up and down as the wheel turns.  the graph is a sine wave, like ripples on the water, like surf on the ocean. no triangles. see the link.

Answer 3

Picture, or draw, a right triangle on a coordinate plane (graph paper).

The base is a line extending some distance along the x axis, say 5 units. The left end of it is at (0,0) the right end of it is at (5,0). A perpendicular line extends up some distance from point (5,0), say to (5,7). This perpendicular line is the other leg of the triangle. The line form (0,0) to (5,7) is the hypotenuse. The angle at (0,0) is most often called "A", and the line opposite it "a". Likewise, the angle at (5,7) is "B" and the base is "b". The right angle is "C" and the hypotenuse is "c".

You already know that sine is a/c, and that as angle A increases from 0 to 90 degrees, sinA increases from 0 to 1.

Think of point B as tracing out a circle as it rotates around point A, with the hypotenuse of the ever-changing triangle being the radius of the circle. When point B enters quadrant II sine decreases from 1 to 0. Then in quadrant III sine decreases from 0 to -1. And, finally, in quadrant IV sine increases from -1 to 0.

Do not think of angle A as increasing from 0 to 90 degrees in quadrant I then decreasing from 90 to 0 degrees in quadrant II, and repeating this pattern in quadrants III and IV. Rather, after increasing from 0 to 90 degrees in quadrant I, it increases from 90 to 180 degrees in quadrant II, then from 180 to 270 degrees in quadrant III, and, finally to 360 degrees in quadrant IV. It has come full circle.

To graph sine, the y-axis represents the numerical value of sinA, while the x-axis represents angle A in degrees. Here are the values you should get from your calculator when entering sinA.

sin0* = 0, sin90* = 1, sin180* = 0, sin 270* = -1, sin 360* = 0

Using additional values between these these angles (ie. 30*, 45*, 60*, etc.), your graph should look like a smooth wave varying between 1 and -1.

You can use similar procedures to graph cosA, tanA, cotA, secA, and cscA. You might be surprised at some of the graphs.

  

Answer 4

Sine is plotted similar to a wave on an ocean, with the intercept falling at (0, 0). You must remember that a graph represents an entire series of answers.

For Sine(x), when x = 0°, f(x) = 0

when x = 90°, f(x) = 1

Each value of X has it's own value between -1 and 1 in a sideways S shape that repeats indefinitely. If you are still confused, I would suggest checking out some graphs at wikipedia.

Answer 5

Consider a unit circle (circle with radius = 1).

The 0 deg is to the right, and angles increase counterclockwise.

Now, as you increase the angle, you can form a triangle between the 0 deg line, the radius (hypotenuse) and a vertical. The sine graph graphs the value of the sine of the angle as you increase the angle and change the triangle.

This is a bit difficult to understand from just words. Take a look at the links below, hopefully it will help.