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Trigonometric Relationships

Today you will need:

  1. Notes
  2. Calculator, Ruler & Protractor
  3. Positive Attitude! :-)

Grab a warm-up from the wooden desk and get started!

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Goals:

  • Solidify understanding of proportional side relationships of similar right triangles
  • develop procedural fluency using trigonometric ratios to solve problems.

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Warm-up #1

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Warm-up #1 KEY

The opposite side from the reference angle.

This helps us identify the trig relationship that’s needed!

opposite side

opposite

opposite

adjacent

adjacent

hypotenuse

hypotenuse

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Warm-up #2

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Warm-up #2

KEY

x = 3.5

x = 7.52

x = 40

x = 20

x = 7.52

x = 40

opposite

adjacent

hypotenuse

adjacent

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SOH CAH TOA

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Trigonometry

Reference Angle

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What do you notice?

Do you think this will ALWAYS hold true?

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IXL.com

Trig Ratios: Sin, Cos, and Tan (VLY)

Trig Ratios with Radicals: Sin, Cos, Tan (D5Z)

Trig Ratios: Find a side length (UZC)

Sine and Cosine of complementary angles (KMH)

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Practice Day

Today you will need:

  • Calculator (in degree mode)
  • Chromebook
  • Positive Attitude! :-)

Grab a warm-up from the wooden desk

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Goals:

  • Solidify understanding of proportional side relationships of similar right triangles
  • develop procedural fluency using trigonometric ratios to solve problems.

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Warm-up #1

Find the value of x. Round your answer to the nearest tenth.

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Warm-up #2

Find the value of x. Round your answer to the nearest tenth.

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Warm-up #2

The following is a list of conjectures made by students about right triangles and trigonometric relationships. For each, state whether you think the conjecture is true or false. Justify your answer.

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IXL.com

Trig Ratios: Sin, Cos, and Tan (VLY)

Trig Ratios with Radicals: Sin, Cos, Tan (D5Z)

Trig Ratios: Find a side length (UZC)

Sine and Cosine of complementary angles (KMH)

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IXL.com

Log on to IXL.com and complete the following:

D5Z

UZC

Want some extra practice with special right triangles?

LDM

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Independent Practice

G14: Triangles 2

Skills

Video Links

Simple Proportions

Measuring Triangle Sides and Angles

Angle Side Relationship

Identify Triangles of a Given Type

Properties of Isosceles Triangles

Sides of Right Triangles

Ratios of Special Triangles

Right Triangle Proportions

Measure Sides with a Ruler and the Pythagorean Theorem

Identifying Trig Ratios

Identifying Trig Ratios (timed)

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Resources

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Mod 6 Standards

G.SRT.4 Prove and apply theorems about triangles. Theorems include but are not restricted to the following: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.

G.SRT.5 Use congruence and similarity criteria for triangles to solve problems and to justify relationships in geometric figures that can be decomposed into triangles.

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.

G.SRT.7 Explain and use the relationship between the sine and cosine of complementary angles.

G.SRT.8 Solve problems involving right triangles�a. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems if one of the two acute angles and a side length is given.