Teacher Notes    
 

CONCEPT 1 – Explain and use the relationship between the sine and cosine of complementary angles.

 

The trigonometry table can reveal a number of patterns that sometimes get hidden in calculator only use.

 

PATTERN #1 – Identical Sine and Cosine Values

 

If you look at the trigonometry table to the right you see that every sine value has a matching value for cosine. 

 

Why would that happen?

 

Let’s look at the pattern closer….

 

Sin 5° = Cos 85°
Sin 10° = Cos 80°
Sin 23° = Cos 67°
Sin 33° = Cos 57°
Sin 45° = Cos 45°

 

We see that if the two angles are complementary then this relationship works:

 

 

But why does that work?

The answer is quite a simple one.  In a right triangle the two acute angles are always complementary and these two ratios are comparing the exact same sides of the triangle.  Let me show you what I mean.

 

Let us use the example of a 23°, 67° and 90° right triangle.