SOLUTION: Sin2theta+cos4theta

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Question 999084: Sin2theta+cos4theta
Found 2 solutions by fractalier, addingup:
Answer by fractalier(6550) About Me  (Show Source):
You can put this solution on YOUR website!
Let's call theta, q, for simplicity.
sin^2(q) + cos^4(q) =
sin^2(q) + [cos^2(q)]^2 =
sin^2(q) + (1 - sin^2(q))^2 =
sin^2(q) + 1 - 2sin^2(q) + sin^4(q) =
sin^4(q) - sin^2(q) + 1

Answer by addingup(3677) About Me  (Show Source):
You can put this solution on YOUR website!
what do you need the integral or the derivative?
Here's the derivative:
d/dtheta(sin(2)theta+cos(4)theta)
Let's differentiate the terms and factor out the constants:
cos(4)(d/dtheta(theta))+(d/dtheta(theta))sin(2)
(d/dtheta(theta)) sin(2)+cos(4)1 <--- Derivative of theta is 1
cos(4)+1sin(2) Simplify:
cos(4)+sin(2)
---------------
Indefinite integral:
∫(theta*sin(2)+theta*cos(4))dtheta
(sin(2)+cos(4))∫theta d theta
= 1/2theta^2(sin(2)+cos(4))+constant