what is the range of sinx
Answers
Answer:
plus 1 to minus 1
Step-by-step explanation:
Step-by-step explanation:
When x = 0, sin x = 0. As we increase x to 90◦
, sin x increases to 1. As we increase x further,
sin x decreases. It becomes zero when x = 180◦
. It then continues to decrease, and becomes
−1 when x is 270◦
. After that sin x increases and becomes zero again when x reaches 360◦
. We
have now come back to where we started on the circle, so as we increase x further the cycle
repeats.
We can also use this picture to see what happens when x is less than zero. If we decrease x from
zero, sin x decreases. It becomes −1 when x = −90◦
. Then it becomes zero at x = −180◦
, and
1 at x = −270◦
. It then decreases and becomes zero when x = −360◦
. This cycle is repeated if
we decrease x further.
From this picture we can see that, whatever value we pick for x, the value of sin x must always
be between −1 and 1. So the domain of f(x) = sin x contains all the real numbers, but the
range is −1 ≤ sin x ≤ 1. We can also see that the function repeats itself every 360◦
. We can
say that sin x = sin(x + 360◦
). We say the function is periodic, with periodicity 360◦
.
Sometimes we will want to work in radians instead of degrees. If we have sin x in radians, it is
usually very different from sin x in degrees. For example sin 90◦ = 1 but in radians sin(90) is
about 0.894. We can use a table of values like the one we had before to plot a graph of sin x in
radians. As 2π radians is the same as 360◦
the graph will be very similar to the graph for x in
degrees, but now the labels on the axes have changed.
x 0
π
4
π
2
3π
4
π
5π
4
3π
2
7π
4
2π
sin x 0 0.71 1 0.71 0 −0.71 −1 −0.71 0
1
−1
0
−2π 2π 4π
f(x)
x
f(x) = sin x
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