Math
Unit 4
10th Grade
Lesson 8 of 19
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°.
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.
The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.
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..
Lesson 7
Lesson 9
Topic A: Right Triangle Properties and Side-Length Relationships
Topic B: Right Triangle Trigonometry
Topic C: Applications of Right Triangle Trigonometry
Topic D: The Unit Circle
Topic E: Trigonometric Ratios in Non-Right Triangles