Chapter 4.7 – Inverse Trigonometric Functions

Objectives (click/tap to expand)

- Find exact values of inverse trigonometric functions (without a calculator)
- Use a calculator to approximate inverse trigonometric functions
- Find exact values of composite functions (e.g. arcsin(cos(0)) )
- Analyze graphs of inverse trigonometric functions
- Solve equations
- Simplify composite expressions (e.g. sin(arctan(x)) )

Assessment

No video for Day #35

4-7 Inverse Trigonometric Functions

Watch before Day #36 lesson

Introduction with Inverse Trigonometric Functions (not to be confused with the Reciprocal Trig Functions). Apologies for the scratchy audio -- this was recorded at home instead of my usual classroom "studio."

4-7 Composing Trig & Inverse Trig Functions

Watch before Day #37 lesson

Plugging an inverse trig expression into a trig expression and getting an algebraic (non-trig) output

4-7 Viewing Angle

Optional for after Day #37 lesson

Here is the Viewing Angle handout, distributed in class as part of this lesson's assignment.

Use inverse trigonometry to help find and then maximize the viewing angle of an object, such as the angle that a large monitor at a stadium forms with your eyeball. This WILL be covered in class, so viewing this video is considered optional. However, in prior years too many students consistently fumbled this question on the test, so I figured it was worth recording this so that the motivated may avoid such a cruel fate.

More "Batman Equation" Exercises (Winter Break)

Here is a pdf of four Transformation Exercises that involve inverse trig functions, and are being used as homework and Do Now exercises.

Similar to "Batman equation" activities of earlier lessons, analyze graphical transformations and develop an equation for a given inverse trigonometric curve.

Out of Phase Circles in GeoGebra

As seen in class, when points orbit a bunch of circles out of phase with each other, you see some interesting effects.

Even though this activity doesn't directly relate to Inverse Trig Functions, I post it on this page since I happened to show it to you while we were studying this chapter.

It would be better to play with this GeoGebra construction on a computer/laptop rather than a cell phone.

Q2 Exam: Format and Practice Questions

The exam covers material through Chapter 4.5. It will be 2 hours for 15 Multiple Choice questions (50% of score) and 9 free response (50% of score). That should be plenty of time if you're well-prepared.

Copies of practice questions will be handed out in class. Answers are on last page.

Download the PDF of the Multiple Choice version here.

Download the PDF of the Short Answer version here.

Suggested Make-it-yourself Practice Exam

- Ch 4.1 -- p358: 13, 21, 25, 27, 29, 45
- Ch 4.2 -- p368: 7, 21, 25, 43, 51
- Ch 4.3 -- p383: 1, 3, 7, 27, 39, 45, 51, 69
- Ch 4.4 -- p394: 3, 11, 15, 21, 31, 39, 59, 65
- Ch 4.5 -- various problems from recent homework; hopefully this stuff is still fresh on your mind
- Review Exercises on p439: 5, 8, 14, 18, 24, 38, 40, 56, 68, 78

Of course, your most recent test should also be considered to be part of your "study guide."

Go to next page, Chapter 4.8.

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