Question 1183085: Sketch sinx and its inverse on the same set of axes for 0≤ x ≤ (pi/2)
I sketched sinx but I don't know how to sketch it's inverse on the same axis, as for its inverse I know that when x = 1, y = (pi/2) but I already put the radians unit on the x axis.
Found 2 solutions by Theo, math_tutor2020:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! putting them on the same axis is tricky, but it can be done.
we'll work in radians.
the graph of y = sin(x) is shown below.
the graph of y = sin^-1(x) is shown below:
the difficulty is that:
when you graph y = sin(x), x is the angle and y is the trig function value.
when you graph y = sin^-1(x), x is the trig function value and y is the angle.
to graph them on the same axes, let the x-axis remain as the angle.
the functions are y = sin(x) and y = sin^-1(sin(x)).
that graph looks like this:
the blue graph is y = sin(x).
the red graph is y = sin^-1(x).
when x = pi/2, y = sin(x) = 1 and y = sin^-1(sin(x)) = pi/2, as shown on the graph.
the coordinate point for y = sin^-1) is shown as (pi/2,pi/2)
that means the x-value is pi/2 and the y-value is pi/2).
the x-value is pi/2, which is the angle.
y = sin(x) is equal to 1.
the coordinate points are (pi/2,1)
this is what is shown on the blue graph.
y = sin^-1(sin(x)) is equal to sin^-1(1) which is equal to pi/2.
the coordinate points are (pi/2,pi/2)
this is what is shown on the red graph.
keep in mind that the function y = sin^-1(sin(x)) will always make the value of y equal to the value of x.
not matter what value of x you choose, y will always be equal to x.
for example, if x = pi/4, sin(pi/4) = .7071067812.
sin^-1(.7071067812) = .7853981634.
divide that by pi and it becomes .25 * pi which is the same as pi/4.
sin-1(sin(pi/4) is equal to pi/4.
sin^-1(sin(pi/2) is equal to pi/2 as shown on the graph.
Answer by math_tutor2020(3817)  (Show Source):
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