Aim: How do we define the inverse of y = sin x as y = Arc sin x?

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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

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

y = arc sin x y = x or y = sin x

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

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

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

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

Notice that is equivalent to is equivalent to

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

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