Sec. 4.7a

Reminders… What does it mean for a function to be one-to-one???  It passes both the vertical and horizontal line tests What does it mean for a function to pass the HLT???  It has an inverse that is also a function Are any of the six basic trigonometric functions one-to-one???  If not, then how do they have inverse functions? NOPE!!! We first r rr restrict the domain of the basic function…

Inverse Sine Function=arcsine We restrict the domain of to the interval 1 –1 1 The unique angle y in the interval such that is the inverse sine (or arcsine) of x, denoted or. The domain of is and the range is

Guided Practice Find the exact value of each expression without a calculator. 1. Note: The values of will always be found on the right-hand side of the unit circle, between. We find the point on the right half of the unit circle whose y-coordinate is 1/2 and draw a reference triangle: Do we recognize this angle???

Guided Practice Find the exact value of each expression without a calculator. 2. Draw another reference triangle, and identify the angle… 3. The domain of the inverse sine function is [–1,1], and, so… DNE

Guided Practice Find the exact value of each expression without a calculator. 4. Draw an angle of in standard position and mark its y-coordinate on the y-axis. The angle in the interval whose sine is this number is.

Guided Practice Find the exact value of each expression without a calculator. 5. Draw an angle of in standard position and mark its y-coordinate on the y-axis. The angle in the interval whose sine is this number is.

Inverse Cosine Function=arccosine We restrict the domain of to the interval 1 –1 The unique angle y in the interval such that is the inverse cosine (or arccosine) of x, denoted or. The domain of is and the range is 1–1

Inverse Tangent Function=arctangent We restrict the domain of to the interval The unique angle y in the interval such that is the inverse tangent (or arctangent) of x, denoted or. The domain of is and the range is

Guided Practice Find the exact value of each expression without a calculator. 6. Note: The values of will always be found on the top half of the unit circle, between 0 and. We find the point on the top half of the unit circle whose x-coordinate is and draw a reference triangle: Do we recognize this angle???

Guided Practice Find the exact value of each expression without a calculator. 7. We find the point on the right side of the unit circle whose y-coordinate is times its x-coordinate and draw a reference triangle: Do we recognize this angle??? Note: The values of will always be found on the right-hand side of the unit circle, between (but not including).

Guided Practice Find the exact value of each expression without a calculator. 8. Draw an angle of –1.1 in standard position, and mark its x-coordinate on the x-axis. The angle in the interval whose cosine is this number is 1.1…