Trigonometric Identity: Double Angle.

[Jessbek]

Homework Statement

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.

Homework Equations

sin 2 ∅ = 2 ((sin ∅) (cos ∅)

The Attempt at a Solution

Attempt? I've tried deriving the double angle equation but can't get anywhere... :( basically there is only one known piece of info (in the hypotenuse being one unit in length)...

 

[LCKurtz]

Homework Statement

Here is the question given:

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

View attachment 47006

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.

Homework Equations

sin 2 ∅ = 2 ((sin ∅) (cos ∅)

The Attempt at a Solution

Attempt? I've tried deriving the double angle equation but can't get anywhere... :( basically there is only one known piece of info (in the hypotenuse being one unit in length)...

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.

 

[Jessbek]

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.

I know what you mean and thank you.

But what I don't know is what to do from there to get some physical/actual answer...

 

[LCKurtz]

I know what you mean and thank you.

But what I don't know is what to do from there to get some physical/actual answer...

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.

 

[Jessbek]

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.

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

 

[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.

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

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.

 

[Jessbek]

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.

I know and this is what confuses me. You can express the area in terms of $\phi$ yes, but this won't get me anywhere. I have written the question essentially the same, so maybe there is an error with the question.