Exploring Trigonometric Ratios

Topic:
Ratios

G-SRT.3.6

In this activity, students will relate the definitions of trigonometric ratios to a property of similar triangles.

Triangle ADE

Note that dragging E moves Line DE along Ray AB. Line DE was constructed to be perpendicular to Ray AB. This makes Triangle ADE a right triangle.

As you drag E, Triangle ADE is changed, but what relationship exists between all these versions of Triangle ADE?

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Note that dragging C changes the measure of Angle A.

As you drag C, Triangle ADE is changed, but what relationship exists between all these versions of Triangle ADE?

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Exploring Trigonometric Ratios Worksheet (don't worry about this if you've received the worksheet in class)

Use this to complete the tables 1 and 3 on the Exploring Trigonometric Ratios Worksheet

Answer this question after you've completed Table 1.

When you compared the values in Table 1 to values in a trigonometric table, what column did they match with?

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Table 1

What did you observe about the multiple trials using the same angle in Table 1?

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Answer this question after you've completed Table 3.

When you compared the values in Table 3 to values in a trigonometric table, what column did they match with?

Check your answer here

Table 3

What did you observe about the multiple trials using the same angle in Table 3?

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VOCABULARY

Remember that complementary angles add up to 90 degrees.

Compare the values in table 1 to the values of the complementary angles in table 2.

What do you notice?

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