Curriculum / Math / 10th Grade / Unit 4: Right Triangles and Trigonometry / Lesson 15
Math
Unit 4
10th Grade
Lesson 15 of 19
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Lesson Notes
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Use the first quadrant of the unit circle to define sine, cosine, and tangent values outside the first quadrant.
The core standards covered in this lesson
F.TF.A.2 — Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.
The foundational standards covered in this lesson
8.G.A.1 — Verify experimentally the properties of rotations, reflections, and translations:
The essential concepts students need to demonstrate or understand to achieve the lesson objective
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
25-30 minutes
Given a 30° angle on the unit circle,
a) Find the coordinate point of this angle. b) Reflect this point over the y-axis.
How is $${-\mathrm{sin}(45^\circ)}$$ different from $${\mathrm{sin}(-45^\circ)}$$? Use your unit circle to help determine this.
Given a 60° angle on the unit circle,
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
Below is a unit circle. The points marked on the circle represent the intersection of the terminal sides of the reference angles of 30°, 45°, and 60°. Write the coordinates for all of the marked points around the unit circle.
Unit Circle with Reference Triangles by Match Foundation, Inc. is made available by Desmos. Copyright © 2017 Desmos, Inc. Accessed March 13, 2017, 4:27 p.m..
The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.
Next
Derive the area formula for any triangle in terms of sine.
Topic A: Right Triangle Properties and Side-Length Relationships
Define the parts of a right triangle and describe the properties of an altitude of a right triangle.
Standards
G.CO.A.1G.SRT.B.4
Define and prove the Pythagorean theorem. Use the Pythagorean theorem and its converse in the solution of problems.
G.SRT.B.4
Define the relationship between side lengths of special right triangles.
G.SRT.B.4G.SRT.B.5
Multiply and divide radicals. Rationalize the denominator.
A.SSE.A.2N.RN.A.2
Add and subtract radicals.
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Topic B: Right Triangle Trigonometry
Define and calculate the sine of angles in right triangles. Use similarity criteria to generalize the definition of sine to all angles of the same measure.
G.SRT.C.6
Define and calculate the cosine of angles in right triangles. Use similarity criteria to generalize the definition of cosine to all angles of the same measure.
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°.
G.SRT.C.7
Describe and calculate tangent in right triangles. Describe how the value of tangent changes as the angle measure approaches 0°, 45°, and 90°.
G.SRT.C.6G.SRT.C.7
Solve for missing sides of a right triangle given the length of one side and measure of one angle.
G.SRT.C.8
Topic C: Applications of Right Triangle Trigonometry
Find the angle measure given two sides using inverse trigonometric functions.
Describe the relationship between slope and the tangent ratio of the angle of elevation/depression. Use the tangent ratio of the angle of elevation or depression to solve real-world problems.
Solve a modeling problem using trigonometry.
Topic D: The Unit Circle
Define angles in standard position and use them to build the first quadrant of the unit circle.
F.TF.A.2
Topic E: Trigonometric Ratios in Non-Right Triangles
G.SRT.D.9
Verify algebraically and find missing measures using the Law of Sines.
G.SRT.D.10
Verify algebraically and find missing measures using the Law of Cosines.
Use side and angle relationships in right and non-right triangles to solve application problems.
G.SRT.D.11
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