Derive the relationship between sine and cosine of complementary angles in right triangles, and describe sine and cosine as angle measures approach 0°, 30°, 45°, 60°, and 90°.
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Below are three right triangles. Assume the value of the hypotenuse of each triangle is $$1$$.
a) Using what you know about special right triangles, find the length of each side.
b) Fill in the chart describing the sine and cosine of each measure below.
$${\mathrm{sin}(30^\circ)}$$ | $${\mathrm{sin}(45^\circ)}$$ | $${\mathrm{sin}(60^\circ)}$$ |
$${\mathrm{cos}(30^\circ)}$$ | $${\mathrm{cos}(45^\circ)}$$ | $${\mathrm{cos}(60^\circ)}$$ |
Using the cosine and sine values from the table in Anchor Problem #1, identify trigonometric ratios that are the same. Then, write a conjecture about how the sine is related to the cosine of complementary angles.
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The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.
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FInd the value of $${\theta}$$ that makes each statement true.
$$\mathrm{sin}{\theta}=\mathrm{cos}32$$
$$\mathrm{cos}{\theta}=\mathrm{sin}({\theta}+20)$$
Geometry > Module 2 > Topic E > Lesson 27 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..