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Finding Sine
Resource ID#: 73174
Primary Type: Formative Assessment
This document was generated on CPALMS - www.cpalms.org
Students are asked to explain the relationship between sine and cosine of complementary angles.
Subject(s): Mathematics
Grade Level(s): 9, 10, 11, 12
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, sine, cosine, right triangles, complementary angles
Instructional Component Type(s): Formative Assessment
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_FindingSine_Worksheet.docx
MFAS_FindingSine_Worksheet.pdf
FORMATIVE ASSESSMENT TASK
Instructions for Implementing the Task
This task can be implemented individually, with small groups, or with the whole class.
1. The teacher asks the student to complete the problem on the Finding Sine worksheet.
2. The teacher asks follow-up questions, as needed.
TASK RUBRIC
Getting Started
Misconception/Error
The student does not understand the properties of a right triangle or the definitions of the trigonometric ratios.
Examples of Student Work at this Level
The student:

Attempts to find angle measure of , but inputs

Incorrectly identifies the sine ratio as

Finds the sine ratio of and writes sin = .
Labels the lengths of the sides of the triangle and then finds sin .

into the calculator and writes that
and writes that
or as
= 0.01.
and writes sin
=
.

Finds the measure of , and writes that
.


Writes sin is the reciprocal of the cos , that is,
.
Labels the lengths of the sides of the triangle incorrectly and, consequently, describes the sin
incorre
Questions Eliciting Thinking
What are you trying to find when asked, "What is sin "?
Are you looking for the ratio of sides or the angle measure?
How would the question have been written if you were to find the angle measure?
What ratios of sides of a right triangle are represented by sine, cosine, and tangent?
Based on the given cosine ratio, which side has a length of 3 and which side has a length of 5?
Can you demonstrate how you determined
was the sine ratio for ?
Will you demonstrate for me how you arrived at your answer?
Do you think sin
could equal cos ? Why or why not?
Instructional Implications
Review with the student the vocabulary associated with right triangles (e.g. right, acute, and complementary a
ratios for each acute angle. If needed, include right triangles in different orientations. Remind the student that
label the length of each side and the measures of the angles ( and ). Have the student write the other two trig
Review with the student the difference between finding a ratio of sides and a degree measure of an angle. Pro
determine what needs to be found and then solve the problem. Review with the student when a calculator is n
Using a calculator, have the student complete a chart of the sine and cosine ratios of several pairs of complem
ratios are equal. Emphasize that the side adjacent to one acute angle of a right triangle is the same side as the
out that the "co" in cosine refers to the sine of its complement.
Moving Forward
Misconception/Error
The student does not understand the relationship between
and .
Examples of Student Work at this Level
The student:


Does not respond to the second question.
Writes that both angles are congruent.

Writes that both angles are equal to
Writes that both angles are
.

and are therefore equal to each other.

Writes that the angles are supplementary.
Questions Eliciting Thinking
If both acute angles in a right triangle are equal, what is true about their measures?
What do you know about the side lengths of a 45-45-90 triangle?
If the side opposite one angle in a triangle is greater than the side opposite another angle, what must be true ab
If two angles are congruent in the same triangle, what type of triangle is it? Is this triangle isosceles?
What is the definition of supplementary angles?
Instructional Implications
Have the student calculate the measure of and using his or her calculator. If needed, review with the stude
triangles with given side lengths. Using a calculator, ask the student to make a chart listing the measures of th
remember this relationship by pointing out that the "co" in cosine refers to the sine of its complement. If need
If the student writes 0.6 as his or her answer to the first question, make sure he or she understands that a ratio,
Almost There
Misconception/Error
The student does not include that
and
are complementary in his or her reasoning about what is true regard
Examples of Student Work at this Level
The student writes:

The angle measures must be different.


The angles must lie in the same right triangle.
That must be greater than because it lies opposite the longer side.
Questions Eliciting Thinking
Is there anything else that you know about the measures of the two acute angles of a right triangle?
Instructional Implications
Guide the student to observe that the two acute angles of a right triangle are complementary. If needed, review
Provide the student with the definitions of the secant, cosecant, and cotangent ratios. Ask the student to write
student if he or she sees a similarity in the names of the ratios that are equal. Help the student remember this r
If the student writes 0.6 as his or her answer to the first question, make sure he or she understands that a ratio,
Got It
Misconception/Error
The student provides complete and correct responses to all components of the task.
Examples of Student Work at this Level
The student writes that sin
=
. The student understands that the side adjacent to one acute angle of a right
The student also writes that angles
and
are complementary. The student understands that
Questions Eliciting Thinking
The sin 15° = cos x°. What is the value of x?
If
, what does
equal?
If
, are there any angle measures for which sin
= cos ? If yes, what are they? If not, why not?
Instructional Implications
Provide the student with the definitions of the secant, cosecant, and cotangent ratios. Ask the student to write
student if he or she sees a similarity in the names of the ratios that are equal. Help the student remember this r
Challenge the student to use his or her understanding of the Pythagorean Theorem to explain why
ACCOMMODATIONS & RECOMMENDATIONS

Special Materials Needed:
o
Finding Sine Worksheet
SOURCE AND ACCESS INFORMATION
Contributed by: MFAS FCRSTEM
Name of Author/Source: MFAS FCRSTEM
District/Organization of Contributor(s): Okaloosa
Is this Resource freely Available? Yes
License: CPALMS License - no distribution - non commercial
Related Standards
Name
MAFS.912.G-SRT.3.7:
Description
Explain and use the relationship between the sine and cosine of
complementary angles.