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6.5.2 – Inverse Trig Functions Applications and Other Expressions

6.5.2 – Inverse Trig Functions Applications and Other Expressions. On some occasions, you will still be required to make certain calculations without using a calculator Yesterday, we talked about evaluating trig functions within trig functions. Example. arcsin (sin( π /4)).

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6.5.2 – Inverse Trig Functions Applications and Other Expressions

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  1. 6.5.2 – Inverse Trig Functions Applications and Other Expressions

  2. On some occasions, you will still be required to make certain calculations without using a calculator • Yesterday, we talked about evaluating trig functions within trig functions. • Example. arcsin(sin(π/4))

  3. We can still do the same without a calculator • Familiar with the table we used to form the graphs • Use the first quadrant/reference angles to help you determine the values you need to “backtrack” • Example. Find the value of sin(arctan(√3))

  4. Example. Evaluate the expression cos(cot-1(-1)) • Example. Evaluate the expression: cot(arcsin(-√2/2))

  5. Algebraic Functions • We still may use some trig functions in the sense of an algebra function • Inverse operations • Solve for x • Just need to apply similar properties and bare in mind the ratios for the trig functions we learned earlier this semester

  6. When working with the algebraic functions, just keep in mind what operations you need to solve for x

  7. Example. Express the following as an algebraic function: tan(cos-1(x))

  8. Example. Express the following as an algebraic function: sec(tan-1(3x))

  9. Applications • Inverse trig functions may be used in any application involving a missing angle of interest • What you need to know to find angles: • 1) At least 2 sides • 2) Two sides and an angle

  10. Example. A pumpkin is launched in the air. The maximum height is calculated as 50 feet. The pumpkin traveled 30 feet when it reached it’s maximum height. Find the angle the pumpkin was launched at.

  11. Example. A lacrosse player is approximately 8 yards from the goal when he shoots. The ball travels approximately 12 yards to reach the goal. Find the angle he shoots at to the goal.

  12. Come up with your own problem involving using inverse functions. Then, share with 2 other people.

  13. Assignment • Pg. 528 • 53-69 odd • 70, 77

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