Inverse Trigonometric Functions Sec 4 7 a Reminders
- Slides: 12
Inverse Trigonometric Functions Sec. 4. 7 a
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? ? ? NOPE!!! If not, then how do they have inverse functions? We first restrict the domain of the basic function…
Inverse Sine Function=arcsine We restrict the domain of to the interval 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. DNE The domain of the inverse sine function is [– 1, 1], and , so…
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 We restrict the domain of Function=arccosine to the interval 1 – 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
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. Note: The values of will always be found on the right-hand side of the unit circle, between (but not including). 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? ? ?
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…
- Summary of inverse trigonometric functions
- 4-6 practice inverse trigonometric functions answer key
- Integral of logarithmic functions
- Arcsin meaning
- Arctan equation
- Properties of inverse functions
- Integration of inverse trigonometric functions
- Inverse laplace transform of trigonometric functions
- Inverse circular functions
- Ehr alerts and reminders
- Staar reminders
- Wcms dress code
- Math reminders