Describe and calculate tangent in right triangles. Describe how the value of tangent changes as the angle measure approaches 0°, 45°, and 90°.
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Memorization of the tangent for common angle measures is not required by the Common Core standards. However, if students have these values memorized, they will be better able to access some Algebra 2 and AP Calculus material.
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Below is a set of similar right triangles. Find the ratio of the side lengths within each triangle that describe the side opposite the marked angle divided by the side adjacent to the marked angle.
What is the tangent of 0°, 45°, 60°, and 90°? Describe why the tangent of 90° is undefined.
For a right triangle, is the following statement always, sometimes, or never true?
$${\mathrm{tan}\theta=\frac{\mathrm{sin}\theta}{\mathrm{cos}\theta}}$$
Geometry > Module 2 > Topic E > Lesson 30 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..
Modified by Fishtank Learning, Inc.?
The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.
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If $${\mathrm{sin}\theta=\frac{\sqrt5}{5}}$$, find $${\mathrm{cos}\theta}$$ and $${\mathrm{tan}\theta}$$.
Geometry > Module 2 > Topic E > Lesson 30 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..