1. Aim: How do we define the inverse of y = sin x as y = Arc sin x?
Do Now: Given f(x) = sin x,
a) fill in the table below:
b) write the coordinates of each point after reflected in y = x x
f(x)
HW: p.424 # 15,21,22,28,29,32,33,37

2. The coordinates of each point after reflected in y = x
are
These points are the inverse of y = sin x
If we connect those points, the graph is called
y = arc sin x or

3. y = arc sin x
y = x or
y = sin x

4. For y = sin x, the Domain = {
Real numbers}
Range = { }
Domain = { }
Range = {
real numbers}
a function ? Is
Generally NO (It fails the vertical line test)

5. But if we limit the domain then it can be a function over that particular range.
If the domain is
the relation
IS a function.
We use y = Arc sin x or to represent the inverse that is a function.
That is, is only limited in quadrants I and IV only

6. Therefore, y = arcsin x is a function only within -½π ≤ x ≤ ½π
We use y = Arcsin x or
y = Sin-1 x to represent
Finally, the inverse function of y = sin x only defined in quadrant I and IV

7. ,since 30 is in quadrant I or 150 Which one is true?
The idea between the function and inverse function is

8. Notice that
is equivalent to
is equivalent to

9. If 2. If , find the value of 3. If , find the value of 4. If 5. If
, write the equivalent function
2. If
in degrees.
, find the value of If
in radians.
3. If
, find the value of
4. If
in radians.
, find the value of
5. If
in radians.
, find the value of

10. 6. Find the exact value of if the angle is a third-quadrant angle.
9. Find θ to the nearest degree