Ratios in Right Triangles

The "Introduction" reviews the Pythagorean theorem. "Naming Sides" reviews the trigonometry triangle names required to use "Soh Cah Toa". The "Practice" section has 5 sections of problem types. For this activity complete problem types 1 - 3. The activity below this one focuses on the same 3 problem types.

Problem Types 1-3: Pythagorean Theorem.
Problem Types 4-6: Calculate the sine, cosine and tangent ratios given one reference angle.
Problem Types 7-9: Calculate the sine, cosine and tangent ratios given two appropriate sides.
Problem Types 10-12: Calculate the reference angle given two appropriate sides.
Problem Types 13-18: Calculate the length of one of the sides given appropriate side and reference angle.

Review:

We can use trigonometry functions to determine:

one acute angle if you know two sides
one of the sides if you know an acute angle and one side

To remember the trigonometry functions, use the memory aid:

Soh Cah Toa

The first letter of each aid represents the function. The last two letters indicates the ratio of sides needed to calculate the function.

Soh --> Sine = opposite/hypotenuse

Cah --> Cosine = adjacent/hypotenuse

Toa --> Tangent = opposite/adjacent

sine cosine tangent

Enrichment:

Sine Cosine Tangent

What is the pattern of Sine, Cosine, and Tangent as you increase the angle from 0 to 90^o? Use the radio buttons to select Sine, Cosine, or Tangent. Move the radius of the circle (hypotenuse of the right triangle) from 0 to 90^o and observe what happens to the ratio! Check the text below to make sure you understand the pattern for each trigonometry ratio..

Java Applet compliments of Walter Fendt

Trignometry Waves There is beauty and pattern in trigonometry. Click on "Start" and watch the wave generated for each trigonometyr function. What pattern do you observe for each function? Which two functions produce similar waves?
Sine	[Applet appears here for Java-capable browsers]	The sine wave starts at 0, moves up to 1, down to -1 and then back to 1. The pattern continues with the wave moving between 1 and -1.
Cosine	[Applet appears here for Java-capable browsers]	The cosine wave starts at 1, moves down to 0, continues down to -1 and then back to 1. The pattern continues with the wave moving between 1 and -1. The wave generated looks very much like the sine wave.
Tangent	[Applet appears here for Java-capable browsers]	The tangent wave starts at zero, increases to infinitely positive, then moves down to infinitely negative. The pattern continues with the wave moving between infinitely positive and infinitely negative.
source author: J. David Eisenberg

Ferris Wheel Tracing Sinusoidal Curve

Can you see the sinusoidal curve traced out by the ferris wheel. Click on the ferris wheel to study the pattern in more detail..

Ferris Wheel

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