Manipulating Equations with Trigonometric Identities

[shreddinglicks]

Homework Statement

I just want to manipulate this equation

Homework Equations

8 - {[(4(rcos(x))^2 +4(rsin(x)^2)^2] / 2}

I should have:

8-8r^4

The Attempt at a Solution

I used FOIL and the Pythagorean identity to get:

8- {[16r^4 + (32r^4sin(x)^2cos(x)^2)] / 2}

which is wrong

 

[LCKurtz]

Homework Statement

I just want to manipulate this equation

Homework Equations

8 - {[(4(rcos(x))^2 +4(rsin(x)^2)^2] / 2}

I should have:

8-8r^4

The Attempt at a Solution

I used FOIL and the Pythagorean identity to get:

8- {[16r^4 + (32r^4sin(x)^2cos(x)^2)] / 2}

which is wrong

Use the basic trig identity involving $\sin^2x$ and $\cos^2 x$ before expanding.

 

[Mark44]

Homework Statement

I just want to manipulate this equation

Homework Equations

8 - {[(4(rcos(x))^2 +4(rsin(x)^2)^2] / 2}

That's not an equation. The tipoff that it isn't an equation is that no = sign appears anywhere in this expression.

 

[shreddinglicks]

Thanks, I got the answer. Much easier than what I did the 1st time.

 

[shreddinglicks]

That's not an equation. The tipoff that it isn't an equation is that no = sign appears anywhere in this expression.

It's part of an equation.

 

[Mark44]

It's part of an equation.

Not relevant.

What you said was "I just want to manipulate this equation." but what you showed is not an equation. That was my point. It's not a major thing, but it is important to get the terminology right so as to be able to communicate effectively.

 

[BiGyElLoWhAt]

Also, I believe you typed your equation wrong.
you typed:
8 - {[(4(rcos(x))^2 +4(rsin(x)^2)^2] / 2}
I think you meant to type
8 - {[(4(rcos(x))^2 +4(rsin(x)^2)]^2 / 2}