Trigonometric ratios and functions, the unit circle, inverse trig functions, identities, trig graphs, etc.
Skylar
Posts: 2
Joined: Thu Feb 02, 2012 5:20 am
Contact:

how can i simplify this equation using trig identities/formulas:

cosy = sqrt{sin4x + 4cos2x} - sqrt{cos4x + 4sin2x}

stapel_eliz
Posts: 1628
Joined: Mon Dec 08, 2008 4:22 pm
Contact:
cosy = sqrt{sin4x + 4cos2x} - sqrt{cos4x + 4sin2x}
What are you given as the relationship between "x" and "y"? Thank you!

Skylar
Posts: 2
Joined: Thu Feb 02, 2012 5:20 am
Contact:

I think we are just supposed to simplify the expression on the right side of the equation. The instructions are to "express y in terms of x"

stapel_eliz
Posts: 1628
Joined: Mon Dec 08, 2008 4:22 pm
Contact:
I think we are just supposed to simplify the expression on the right side of the equation. The instructions are to "express y in terms of x"
Then you're not supposed to simplify; you're supposed to solve for y.

A good start will be to apply the Pythagorean Identity to the quadric terms. For instance, restate (cos2(x))2 in terms of sine, and then combine with the other sine term inside that square root. And so forth.

Once you have the right-hand side simplified somewhat, you can take the inverse.