Trig Conversion: Learn How to Go from One Form to the Other

[hayesk85]

Homework Statement

My book does not explain how to go from one form to the other

Homework Equations

sin(2x)cos(2x) = ¹/₂sin(4x)

 

[Hootenanny]

Homework Statement

My book does not explain how to go from one form to the other

Homework Equations

sin(2x)cos(2x) = ¹/₂sin(4x)

Use the double angle trig identity.

 

[Architeuthis Dux]

The solution to this problem is to use the double angle formula for sine, which states that sin(2x) = 2sin(x)cos(x). Therefore, we can rewrite the equation as 2sin(x)cos(x)cos(2x) = 1/2sin(4x). From here, we can use the double angle formula for cosine, which states that cos(2x) = 2cos^2(x) - 1. Substituting this into the equation, we get 2sin(x)cos(x)(2cos^2(x) - 1) = 1/2sin(4x). Simplifying, we get 4sin(x)cos^3(x) - 2sin(x)cos(x) = 1/2sin(4x). Using the half-angle formula for sine, which states that sin(2x) = 2sin(x)cos(x), we can rewrite the equation as 2sin(2x)cos^2(x) - 2sin(x)cos(x) = 1/2sin(4x). Finally, using the double angle formula for sine again, we get sin(4x)cos^2(x) - sin(2x)cos(2x) = 1/2sin(4x). This is the final solution to the problem, and it can be used to convert between the two forms.
Thank you for sharing your solution to the problem. It is important to understand the trigonometric identities and formulas in order to convert between different forms. It might be helpful to review these concepts in your book or consult with your teacher for further clarification. Additionally, practicing more problems will also help improve your understanding and ability to convert between different forms.