MA.912.T.1.1

Define trigonometric ratios for acute angles in right triangles.

Clarifications

Clarification 1: Instruction includes using the Pythagorean Theorem and using similar triangles to demonstrate that trigonometric ratios stay the same for similar right triangles.

Clarification 2: Within the Geometry course, instruction includes using the coordinate plane to make connections to the unit circle.

Clarification 3: Within the Geometry course, trigonometric ratios are limited to sine, cosine and tangent.

General Information
Subject Area: Mathematics (B.E.S.T.)
Grade: 912
Strand: Trigonometry
Status: State Board Approved

Related Courses

This benchmark is part of these courses.
1200400: Foundational Skills in Mathematics 9-12 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1206310: Geometry (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1206320: Geometry Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1206315: Geometry for Credit Recovery (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7912065: Access Geometry (Specifically in versions: 2015 - 2022, 2022 and beyond (current))

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MA.912.T.1.AP.1: Select a trigonometric ratio for acute angles in right triangles limited to sine or cosine.

Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

Formative Assessments

The Sine of 57:

Students are asked to explain what a given sine ratio indicates about a right triangle and if the sine of a specific value varies depending on the right triangle.

Type: Formative Assessment

The Cosine Ratio:

Students are asked to compare the ratio of corresponding sides of two triangles and to explain how this ratio is related to the cosine of a given angle.

Type: Formative Assessment

Sine and Cosine:

Students are asked to explain the relationship between sine and cosine of the acute angles of a right triangle.

Type: Formative Assessment

Right Triangle Relationships:

Students are given the sine and cosine of angle measures and asked to identify the sine and cosine of their complements.

Type: Formative Assessment

Finding Sine:

Students are asked to explain the relationship between sine and cosine of complementary angles.

Type: Formative Assessment

Patterns in the 30-60-90 Table:

Students are asked to use 30-60-90 triangle relationships to observe and explain the relationship between sin 30 and cos 60 (or sin 60 and cos 30).

Type: Formative Assessment

Lesson Plans

Discovering Trigonometric Ratios:

Students investigate and discover trigonometric ratios by drawing and measuring side lengths for five triangles that have equivalent angle measure. Students collect, analyze, and discuss data to draw conclusions. This is the introductory lesson to facilitate student discovery of trigonometric ratios and allows students to secure a solid foundation before the use of trigonometry to find missing sides. This lesson has students solving application problems by finding an unknown angle based on length measurements.

Type: Lesson Plan

Let's Get "Triggy":

This lesson helps students discover trigonometric ratios and how to apply them to find the measure of sides and angles of a right triangle.  Students will think about problems, discuss concepts with a partner and then share ideas with the class. Students will collaborate and offer supportive coaching to help deepen each other’s understanding.

Type: Lesson Plan

MFAS Formative Assessments

Finding Sine:

Students are asked to explain the relationship between sine and cosine of complementary angles.

Patterns in the 30-60-90 Table:

Students are asked to use 30-60-90 triangle relationships to observe and explain the relationship between sin 30 and cos 60 (or sin 60 and cos 30).

Right Triangle Relationships:

Students are given the sine and cosine of angle measures and asked to identify the sine and cosine of their complements.

Sine and Cosine:

Students are asked to explain the relationship between sine and cosine of the acute angles of a right triangle.

The Cosine Ratio:

Students are asked to compare the ratio of corresponding sides of two triangles and to explain how this ratio is related to the cosine of a given angle.

The Sine of 57:

Students are asked to explain what a given sine ratio indicates about a right triangle and if the sine of a specific value varies depending on the right triangle.

Student Resources

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Parent Resources

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