7.1 SOH-CAH-TOA

Sine, Cosine, and Tangent

The trigonometric ratios sine, cosine and tangent refer to the known ratios between particular sides in a right triangle based on an acute angle measure.

Sine, Cosine, and Tangent can be used to identify the measurements of unknown acute angles  A or B  and sides, a, b, or c. 
Note: since this is a Right Triangle we do not need to find the measure of angle C, we know it is 90o.

When we work with right triangles the Pythagorean Theorem ( a2 + b2 = c2 ) usually comes to mind.  We will use the same labeling system for angles and sides when working with sine, cosine and tangent.
Note:  we can use any labels we choose, provided we draw out the triangle and label it!

In this right triangle, side c is the hypotenuse and angle C is the right angle. 

If we consider angle B, then we can describe each of the sides by its position relative to angle B. So then Side a is adjacent to angle B and side b is opposite angle B.

If we consider angle A, then we can describe each of the sides by its position relative to angle A.  So then side b is adjacent to angle A and side a is opposite A

Now we can define the trigonometry ratios as follows:

Let's take another look at our right triangle and identify Sine (Sin), Cosine (Cos), and Tangent (Tan)
If we consider angle B, then we have:

 If we consider angle A, then we have:

 

Example A

Given Right Triangle ABC with side lengths of 3,4,5.

Find the Sine of Angles A & B



Solution:


Watch the video:

 

Quick Question...

Instructions:

  • Identify the Numerator & Denominator for
    the given Trigonometry Ratio
        
  • Use the Blue Slider to set the
    Numerator & Denominator with either the
    Mouse or Left/Right Arrow keys.

To use the app:

  • Clickto begin, click for full screen mode
  • Clickto check your answer.
  • Clickto goto the next problem
  • Clickto stop the app
  

 

Example B

Given Right Triangle ABC with side lengths of 3,4,5.

Find the Cosine of Angles A & B



Solution:

  


Watch the video:

Quick Question...

Instructions:

  • Identify the Numerator & Denominator for
    the given Trigonometry Ratio
        
  • Use the Blue Slider to set the
    Numerator & Denominator with either the
    Mouse or Left/Right Arrow keys.

To use the app:

  • Clickto begin, click for full screen mode
  • Clickto check your answer.
  • Clickto goto the next problem
  • Clickto stop the app
  

Example C

Given Right Triangle ABC with side lengths of 3,4,5.

Find the Tangent of Angles A & B



Solution:


Watch the video:

Quick Question...

Instructions:

  • Identify the Numerator & Denominator for
    the given Trigonometry Ratio
        
  • Use the Blue Slider to set the
    Numerator & Denominator with either the
    Mouse or Left/Right Arrow keys.

To use the app:

  • Clickto begin, click for full screen mode
  • Clickto check your answer.
  • Clickto goto the next problem
  • Clickto stop the app
  

Practice Problems

Given the Right Triangle:
  

A. 

B. 

C. 

 

D.  Do you notice any patterns or similarities between the trigonometric ratios?

 

Assignment:

Instructions:

  • Screenshot each question and paste it into the
    Jamboard and show all work for each  problem.
  • Screenshot the score for each group of question
    onto the group page.

1-3     Do:
4-6     Do:
7-9     Do:

10-12 Do:
13-15 Do:
16-18 Do:

19-21 Do:
22-24 Do:
25-27 Do: