You are now ready to apply your understanding of how trigonometric identities can be used to solve equations. Go to Module 5 Project: Pushing the Limits of Vehicle Performance. Complete Activity 1: Part 2.

 

Save your responses in your course folder.

 

Going Beyond

 

Prosthaphaeresis

 

Before logarithms were used, and much before pocket calculators were invented, product identities were used to estimate the value of products. An example of a product identity is

 

The process is called prosthaphaeresis and can be thought of in four steps:

• Scale down by moving the decimal place of each value so it is between 0 and 1.
• Use cos−1 on each value to determine an A and B value. (Historically this would have been done with a table of cosine values.)
• Use the identity to determine the product.
• Scale up by moving the decimal place to the right (or left) as many places as you moved it to the left (or right) for each input.

Consider 127 × 588.

 

Step 1: 0.127 × 0.588

 

Step 2: = cos (1.4434…) cos (0.9422…)

 

Step 3:

 

Step 4: 74 606

 

So, 127 × 588 = 74 606.