Description
Evaluating INVERSE trigonometric functions [arcsine, arccosine, and arctangent] without a calculator. Students learn how to evaluate inverse trig functions by discovering the domain restrictions through graphing sine, cosine, and tangent functions. Students use Algebra 2 knowledge of one-to-one functions [Vertical & Horizontal Line Tests] and switching domain and range values to graph inverse trig functions. After learning domain restrictions, students turn to the corresponding quadrants on the unit circle to help them find inverse trig ratios. The provided worksheet [32 problems] begins with simple inverse trig evaluations, and then work their way up to double and even triple compositions. Some problems have review of evaluating reciprocal functions [csc, sec, and cot].
THIS ZIP-FILE INCLUDES 26 PAGES.
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✫ CHECK OUT all of my trig reference sheets: Transformations, Graphing, & Inverse Functions
✫ Get a SNEAK PEEK of this lesson in my YouTube video.
✫ THIS PACKAGE IS ALSO INCLUDED IN MY MEGA-BUNDLE:
Evaluate Trig & Inverse Trig Functions / Graph ALL 6 Trig Functions
✫ CHECK OUT MY RELATED BUNDLES:
1) Graphing Sine, Cosine, and Tangent Functions
2) Graphing OTHER Trig Functions [csc, sec, cot, tan]
3) Graphing ALL 6 Trigonometric Functions
4) Unit Circle & Evaluating Trig Functions series
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TOPICS:
➤ The first two pages out of the 11-page packet is foundational Algebra 2 Review of a parabola, where students use the vertical line test [relation is a function] and horizontal line test [inverse relation is not a function] to determine if the function is one-to-one. Feel free to skip these 2 pages if you are under a time constraint.
➤ The Algebra 2 review is important for students as they are presented with sine, cosine, and tangent functions; and learn that none are one-to-one. Thus students need to restrict the domain centered around the origin and choose positive values to make them one-to-one functions.
➤ Students also look at the graphs of inverse trig functions, and understand the graphs since inverse functions have the domain and range switched.
➤ Students realize that whenever they evaluate trig functions, there can only be one solution because of the domain restrictions.
➤ Students connect these domain restrictions to the corresponding quadrants on the unit circle.
➤ The worksheet begins with simple inverse trig evaluations, and then work their way up to double and even triple compositions. Some problems have review of evaluating reciprocal functions [csc, sec, and cot]. All are without using a calculator.
➤ The worksheet also includes 3 problems where students must sketch a right triangle to help them find the correct trig ratio.
INCLUDED:
➤ Step-by-step answer keys / notes to EVERYTHING!
➤ Scaffolded Fill-in-the-Blank Discovery LESSON Packet [11 pages]. The packet also includes 9 examples.
➤ Double-sided worksheet with 32 problems with no calculator. The worksheet begins with simple inverse trig evaluations, and then work their way up to double and even triple compositions. Some problems have review of evaluating reciprocal functions [csc, sec, and cot].
➤ 3 Reference sheets; one each for inverse sine, cosine, and tangent functions. It shows visually how to restrict the function for it to be one-to-one and therefore which 2 quadrants we should look at. There's also an "Other Notes" section which details all important review and information.
CHECK OUT MY BUNDLES:
1) Introduction to the Unit Circle
2) Full Unit: Unit Circle, Angles & Radians, Angular/Linear Speed & Arc Length/Area of Sector
3) Introduction & Graphing Sine and Cosine Functions
4) Graph Sine, Cosine & Tangent Functions Step-by-Step
5) Graphing Other Trig Functions [tan, cot, sec, csc]
6) Graphing ALL 6 Trigonometric Functions
7) Mega-Bundle: Evaluate Trig & Inverse Trig Functions / Graph ALL 6 Trig Functions
8) Polar & Rectangular Coordinates and Equations
9) Complex Numbers: Polar and Rectangular Forms
10) Full Unit - Complex Numbers [Polar, Rectangular & Euler Forms]
ALSO CHECK OUT: Precalc Midterm Exam with Study Guide
Graph & Evaluate Inverse Trig Functions | Lesson, Worksheet, Reference Sheets
Highlights
Save even more with bundles
Description
Evaluating INVERSE trigonometric functions [arcsine, arccosine, and arctangent] without a calculator. Students learn how to evaluate inverse trig functions by discovering the domain restrictions through graphing sine, cosine, and tangent functions. Students use Algebra 2 knowledge of one-to-one functions [Vertical & Horizontal Line Tests] and switching domain and range values to graph inverse trig functions. After learning domain restrictions, students turn to the corresponding quadrants on the unit circle to help them find inverse trig ratios. The provided worksheet [32 problems] begins with simple inverse trig evaluations, and then work their way up to double and even triple compositions. Some problems have review of evaluating reciprocal functions [csc, sec, and cot].
THIS ZIP-FILE INCLUDES 26 PAGES.
----------------------------------------------------------------------
✫ CHECK OUT all of my trig reference sheets: Transformations, Graphing, & Inverse Functions
✫ Get a SNEAK PEEK of this lesson in my YouTube video.
✫ THIS PACKAGE IS ALSO INCLUDED IN MY MEGA-BUNDLE:
Evaluate Trig & Inverse Trig Functions / Graph ALL 6 Trig Functions
✫ CHECK OUT MY RELATED BUNDLES:
1) Graphing Sine, Cosine, and Tangent Functions
2) Graphing OTHER Trig Functions [csc, sec, cot, tan]
3) Graphing ALL 6 Trigonometric Functions
4) Unit Circle & Evaluating Trig Functions series
----------------------------------------------------------------------
TOPICS:
➤ The first two pages out of the 11-page packet is foundational Algebra 2 Review of a parabola, where students use the vertical line test [relation is a function] and horizontal line test [inverse relation is not a function] to determine if the function is one-to-one. Feel free to skip these 2 pages if you are under a time constraint.
➤ The Algebra 2 review is important for students as they are presented with sine, cosine, and tangent functions; and learn that none are one-to-one. Thus students need to restrict the domain centered around the origin and choose positive values to make them one-to-one functions.
➤ Students also look at the graphs of inverse trig functions, and understand the graphs since inverse functions have the domain and range switched.
➤ Students realize that whenever they evaluate trig functions, there can only be one solution because of the domain restrictions.
➤ Students connect these domain restrictions to the corresponding quadrants on the unit circle.
➤ The worksheet begins with simple inverse trig evaluations, and then work their way up to double and even triple compositions. Some problems have review of evaluating reciprocal functions [csc, sec, and cot]. All are without using a calculator.
➤ The worksheet also includes 3 problems where students must sketch a right triangle to help them find the correct trig ratio.
INCLUDED:
➤ Step-by-step answer keys / notes to EVERYTHING!
➤ Scaffolded Fill-in-the-Blank Discovery LESSON Packet [11 pages]. The packet also includes 9 examples.
➤ Double-sided worksheet with 32 problems with no calculator. The worksheet begins with simple inverse trig evaluations, and then work their way up to double and even triple compositions. Some problems have review of evaluating reciprocal functions [csc, sec, and cot].
➤ 3 Reference sheets; one each for inverse sine, cosine, and tangent functions. It shows visually how to restrict the function for it to be one-to-one and therefore which 2 quadrants we should look at. There's also an "Other Notes" section which details all important review and information.
CHECK OUT MY BUNDLES:
1) Introduction to the Unit Circle
2) Full Unit: Unit Circle, Angles & Radians, Angular/Linear Speed & Arc Length/Area of Sector
3) Introduction & Graphing Sine and Cosine Functions
4) Graph Sine, Cosine & Tangent Functions Step-by-Step
5) Graphing Other Trig Functions [tan, cot, sec, csc]
6) Graphing ALL 6 Trigonometric Functions
7) Mega-Bundle: Evaluate Trig & Inverse Trig Functions / Graph ALL 6 Trig Functions
8) Polar & Rectangular Coordinates and Equations
9) Complex Numbers: Polar and Rectangular Forms
10) Full Unit - Complex Numbers [Polar, Rectangular & Euler Forms]
ALSO CHECK OUT: Precalc Midterm Exam with Study Guide
