Use the identity sin2x = ½ - ½(cos2x)
∫[½ - ½(cos2x)] dx = ∫½ dx - ∫½(cos2x) dx
Let's split it up into ∫½ dx and ∫½(cos2x) dx
∫½ dx = x/2 (we'll put the constant in at the end)
∫½(cos2x) dx (Use u substitution with u=2x and du = 2 dx)
∫cosu ¼du = ¼∫cosu du = ¼sinu + c = ¼sin2x (remember to resubstitute)
Subtract the two parts and add a constant
x/2 - ¼(sin2x) + c
This is also equivalent to: ½(x - sinxcosx) + c
Cosine squared theta = 1 + Sine squared theta
No, they do not.
Your question is insufficiently precise, but I'll try to answer anyway. "Sine squared theta" usually means "the value of the sine of theta, quantity squared". "Sine theta squared" usually means "the value of the sine of the quantity theta*theta". The two are not at all the same.
6,561 (i solved it by using this sentence: (9x9) x (9x9)= 81x81=6,561
It is 1.
The antiderivative of 2x is x2.
Let k = 0 9x18 squared x 17 x 18 k is a constant. Its anti-derivative is kx + C, where C is a constant. The anti-derivative squared is (kx+ C) squared.
Answer 1 Put simply, sine squared is sinX x sinX. However, sine is a function, so the real question must be 'what is sinx squared' or 'what is sin squared x': 'Sin(x) squared' would be sin(x^2), i.e. the 'x' is squared before performing the function sin. 'Sin squared x' would be sin^2(x) i.e. sin squared times sin squared: sin(x) x sin(x). This can also be written as (sinx)^2 but means exactly the same. Answer 2 Sine squared is sin^2(x). If the power was placed like this sin(x)^2, then the X is what is being squared. If it's sin^2(x) it's telling you they want sin(x) times sin(x).
The antiderivative of a function which is equal to 0 everywhere is a function equal to 0 everywhere.
A sine wave is a mathematical function that describes a smooth repetitive oscillation which looks like a wave going from 1 to -1 and back to 1. A normal sine wave is much like a sine wave but has been normalized for practical uses like in electronics creating a "squared" sine wave A perfect sine wave does not exist in reality, it only exists in the minds of mathematicians.