# MAFS.912.G-SRT.3.7

Explain and use the relationship between the sine and cosine of complementary angles.
General Information
Subject Area: Mathematics
Domain-Subdomain: Geometry: Similarity, Right Triangles, & Trigonometry
Cluster: Level 2: Basic Application of Skills & Concepts
Cluster: Define trigonometric ratios and solve problems involving right triangles. (Geometry - Major Cluster) -

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

Date Adopted or Revised: 02/14
Date of Last Rating: 02/14
Status: State Board Approved
Assessed: Yes
Test Item Specifications
Assessed with:

MAFS.912.G-SRT.3.8

## Related Courses

This benchmark is part of these courses.
1200400: Foundational Skills in Mathematics 9-12 (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
1211300: Trigonometry Honors (Specifically in versions: 2014 - 2015, 2015 - 2022 (course terminated))
1206310: Geometry (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
1206320: Geometry Honors (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
1206315: Geometry for Credit Recovery (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
7912065: Access Geometry (Specifically in versions: 2015 - 2022 (current), 2022 and beyond)

## Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MAFS.912.G-SRT.3.AP.7a: Explore the sine of an acute angle and the cosine of its complement and determine their relationship.

## Related Resources

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

## Assessments

Sample 1 - High School Geometry State Interim Assessment:

This is a State Interim Assessment for 9th-12th grade.

Type: Assessment

Sample 4 - High School Geometry State Interim Assessment:

This is a State Interim Assessment for 9th-12th grades.

Type: Assessment

## Formative Assessments

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

Sine and Cosine Relationship between Complementary Angles:

This is a lesson on the relationship between the Sine and Cosine values of Complementary Angles.

Type: Lesson Plan

Sine, Sine, Everywhere a Sine:

This is an inquiry-based learning activity where students use a scientific calculator to compare the values of the sine of an acute angle and the cosine of its complement in a given right triangle.

Type: Lesson Plan

Introduction to Trigonometry:

The video is a brief introduction to or review of trigonometry. The teacher uses a spray bottle to show the difference between opposite, adjacent, and hypotenuse according to the angle in which the bottle is located. Then she touches upon sine, cosine, and tangent. She uses theatrics to introduce the saying "soh-cah-toa" as an acronym for each of the sine, cosine, and tangent.

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.

## Student Resources

Vetted resources students can use to learn the concepts and skills in this benchmark.

## Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.