Sine and Cosine of Complementary Angles

Sine and Cosine of Complementary Angles

The Lesson Activities will help you meet these educational goals:

·  Content Knowledge—You will explain and use the relationship between the sine and cosine of complementary angles.

·  Inquiry—You will perform an investigation in which you will make observations, analyze results, communicate your results in tables and written form, and draw conclusions.

·  21st Century Skills—You will employ online tools for research and analysis, use critical-thinking and problem-solving skills, and communicate effectively.

Directions

You will evaluate some of these activities yourself, and your teacher may evaluate others. Please save this document before beginning the lesson and keep the document open for reference during the lesson. Type your answers directly in this document for all activities.

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Self-Checked Activity

Read the instructions for the following activities and type in your responses. At the end of the lesson, click the link to open the Student Answer Sheet. Use the answers or sample responses to evaluate your own work.

1.  Trigonometric Ratios of Complementary Angles

You will use GeoGebra to explore trigonometric ratios of complementary angles. Go to sine and cosine of complementary angles, and complete each step below. If you need help, follow these instructions for using GeoGebra.

a.  Measure andand find their sum. How are the angles related?

Type your response here:

Angle / Measure

b.  Measure the lengths of the sides of ∆ABC in GeoGebra, and compute the sine and the cosine of and. Verify your calculations by finding the sine and cosine of and using a calculator.

Type your response here:

Side / Length
Angle / sin (GeoGebra) / cos (GeoGebra) / sin (Calculator) / cos (Calculator)

c.  Check the Show sine and cosine of and Show sine and cosine of boxes. Move point B to various locations so that m is approximately 15°, 30°, 45°, 60°, and 75°. In each case, record m and m and record the sine and cosine of and. What relationship do you observe between the sine and cosine of and the sine and cosine of?

Type your response here:

m / m / sin A / cos A / sin B / cos B

d.  Look at ∆ABC and the definitions of sin A and cos A in terms of the side lengths of the triangle. Based on the definitions of sine and cosine, explain what you have observed in the previous parts of this activity. Use equations to support your explanation.

Type your response here:

e.  What general conclusion can you draw about the sines and cosines of complementary angles? State your conclusion in words and in the form of equations.

Type your response here:

How did you do? Check a box below.

Nailed It!—I included all of the same ideas as the model response on the Student Answer Sheet.

Halfway There—I included most of the ideas in the model response on the Student Answer Sheet.

Not Great—I did not include any of the ideas in the model response on the Student Answer Sheet.

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