APS Geometry Unit 4 Book

Wendy Sanchez, Dec 1, 2018

MGSE9-12.G.SRT.6 Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. MGSE9-12.G.SRT.7 Explain and use the relationship between the sine and cosine of complementary angles. MGSE9-12.G.SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

Table of Contents

  1. Trig Ratios using Similarity
    1. Why are right triangles special? (finding angles) APS
    2. Sine vs Cosine Exploration for A Right Triangle
  2. MGSE9-12.G.SRT.6
    1. Exploration: Trigonometric Ratios in Similar Triangles APS
    2. Quiz: Finding Exact Trig Ratios APS
    3. Discovering the Trig Ratios APS
  3. MGSE9-12.G.SRT.7
    1. Practice: Sine and Cosine of Complementary angles APS
    2. Exploration: Sine vs Cosine Exploration in A Right Triangle APS
  4. MGSE9-12.G.SRT.8
    1. Practice: Finding Acute Angles of Right Triangles: Using Inverse Trig Functions APS

1.

Trig Ratios using Similarity

This sketch is can be used with the following standards: [b]MGSE9-12.G.SRT.6[/b] Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. [b]MGSE9-12.G.SRT.7[/b] Explain and use the relationship between the sine and cosine of complementary angles.

  • 1. Why are right triangles special? (finding angles) APS
  • 2. Sine vs Cosine Exploration for A Right Triangle

1.1.

Why are right triangles special? (finding angles) APS

– badboy_wit03

1.2.

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2.

MGSE9-12.G.SRT.6

  • 1. Exploration: Trigonometric Ratios in Similar Triangles APS
  • 2. Quiz: Finding Exact Trig Ratios APS
  • 3. Discovering the Trig Ratios APS

2.1.

Exploration: Trigonometric Ratios in Similar Triangles APS

This demonstration shows trigonometric ratios in right triangles. The program illustrates that the ratio of the lengths of the sides remains constant regardless of the size of the triangle as long as the acute angle is not changed. It allows the user to change both the acute angle and the size of the right triangle.
– S Sharma, Blanca Rubio

2.2.

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2.3.

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3.

MGSE9-12.G.SRT.7

  • 1. Practice: Sine and Cosine of Complementary angles APS
  • 2. Exploration: Sine vs Cosine Exploration in A Right Triangle APS

3.1.

Practice: Sine and Cosine of Complementary angles APS

An Exploration of Sine and Cosine of complementary angles
[br]
INVESTIGATE IT!
[color=#9900ff]Follow the steps below to investigate a special relationship between the sine and cosine of complementary angles. You may work with a partner. [/color]
1. What is the complement of a 35 degree angle?
2. What is the sin(35) expressed as a ratio?
CLICK on the box for the sin(theta) does your ratio you picked above match the calculation for sin(theta)?
CLICK on complementary angle.
3. What is the cos(55) expressed as a ratio?
CLICK on the box for the cos(90-x) does your ratio you picked above match the calculation for cos(90-x)?
4. What do you notice about the sine of an angle and the cosine of its complement (complementary angle)?
THINK:
DRAG Point B to enlarge/shrink the triangle. What do you notice about the sine and cosine of the two different angles?
REFLECT:
1. Uncheck all boxes. [br]2. Click on cos(theta).[br]3. Click on complementary angle, then click on sin(90-theta).[br]4. Does the relationship still hold true?[br]5. Why do you think this is?
– S Sharma, Laina Beale, Susan Socha

3.2.

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4.

MGSE9-12.G.SRT.8

  • 1. Practice: Finding Acute Angles of Right Triangles: Using Inverse Trig Functions APS

4.1.

Practice: Finding Acute Angles of Right Triangles: Using Inverse Trig Functions APS

Quick (Silent) Demo
– S Sharma, Tim Brzezinski

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