# Trigonometric Identity: Double Angle.

1. May 5, 2012

### Jessbek

1. The problem statement, all variables and given/known data

Here is the question given:

A blade for a lawnmower consists of two parts made of the same material and joined together as shown:

The length OP is one unit in length and MPQN is square in shape.

Develop an equation for the cross-sectional area of the blade and find the magnitude of angle ∅ to give the area of the blade.

2. Relevant equations

sin 2 ∅ = 2 ((sin ∅) (cos ∅)

3. The attempt at a solution

Attempt? I've tried deriving the double angle equation but cant get anywhere... :( basically there is only one known piece of info (in the hypotenuse being one unit in length)...

Last edited: May 5, 2012
2. May 5, 2012

### LCKurtz

I guess you mean express the area of the blade in terms of $\phi$. Use trig to express PM and OM in terms of $\phi$, then use that to calculate the two areas.

3. May 5, 2012

### Jessbek

I know what you mean and thank you.

But what I dont know is what to do from there to get some physical/actual answer...

4. May 5, 2012

### LCKurtz

Well, I don't know what else to do either because the statement "find the magnitude of angle ∅ to give the area of the blade" doesn't mean anything to me.

5. May 5, 2012

### Jessbek

I think it simply means find the value of theta, and in turn, use that value to find the surface area of the blade.

6. May 5, 2012

### LCKurtz

But there isn't "a value of $\phi$". As $\phi$ varies so does the area. You can express the area in terms of $\phi$. I think the rest of the problem isn't properly stated.

7. May 5, 2012

### Jessbek

I know and this is what confuses me. You can express the area in terms of $\phi$ yes, but this wont get me anywhere. I have written the question essentially the same, so maybe there is an error with the question.