0
given the identity sin(x+y)=sinx cosy + siny cosx
sin2x = 2 sinx cosx and
sin(2(x)+x) = sin 2x cos x + sinx cos 2x
using the last two identities gives
sin3x= 2 sinx cosx cosx + sinx cos2x
factoring the sinx we have
sin3x = sinx(2cosx cosx+cos2x)
which satisfies the requirement.
However, we can simplify further since cos 2x = cosx cosx - sinx sinx (a well known identity)
sin3x = sinx (2cosx cosx +cosx cosx - sinx sinx)
so sin3x= sinx(3cosx cosx - sinx sinx)
or sin 3x = 3.cos²x.sinx - sin³x
* * * * *
Good, but not good enough. The answer was required in terms of sin, not a mixture of sinx and cosx. Easily recitified, though, since cos²x = 1 - sin²x
Therefore sin3x = 3*(1-sin²x)*sinx - sin³x
= 3sinx - 4sin³x
Still curious? Ask our experts.
Chat with our AI personalities
Jordan
Ezra
ReneAdd your answer:
Earn +20 pts
Derivative of y sin 3x 5?
The derivative of y = sin(3x + 5) is 3cos(3x + 5) but only if x is measured in radians.
Are 3x and x like terms?
Yes, 3x and x are like terms because they have the same variable raised to the same power.
Multiply (x - 6)(3x2 plus 10x - 1)?
Multiply each term of the second expression by each of the terms in the first expression and add them together, collecting like terms together: (x - 6)(3x² + 10x - 1) = x(3x² + 10x - 1) + (-6)(3x² + 10x - 1) = (3x³ + 10x² - x) + (-18x² - 60x + 6) = 3x³ + 10x² - 18x² - x - 60x + 6 = 3x² + (10 - 18)x² + (-1 - 60)x + 6 = 3x² - 8x² - 61x + 6
What is negative x plus 3x?
The expression "negative x plus 3x" can be simplified by combining like terms. Negative x can be written as -1x, so the expression becomes -1x + 3x. When you combine -1x and 3x, you get 2x. Therefore, the simplified expression is 2x.
What is x minus 4x?
The expression "x minus 4x" can be simplified by combining like terms. When subtracting 4x from x, we are essentially subtracting 4 of the x terms from 1 of the x terms, resulting in a final answer of -3x. So, x minus 4x simplifies to -3x.
How do you use the Euler's formula to obtain the sin3X in terms of cosX and sinX?
Using Euler's Formula, you use (cos(x) + i sin(x))^n = cos (nx) + i sin(nx) Now you let n=3 (cos(x) + i sin (x))3 = cos(3x) + i sin (3x) (cos(x))3 + 3(cos(x))2 * i sin(x) + 3cos(x) * i2 (sin(x))3 = cos(3x)+ i sin(3x) (cos(x))3 + i(3sin(x)(cos (x))2) - 3cos(x)(sin(x)2) - i(sin(x))3 = cos (3x) + i sin(3x) Now only use the terms with i in them to figure out what sin(3x) is... 3sin(x)(cos(x))2 - (sin(x))3 = sin(3x) Hope this helps! :D
Parentheses before -1 and after 3x and before 3 and after 3x What is the answer to -2 cos2 3x-3 sin 3x equals 0?
I think you mean to solve:(-2 cos23x) - (3 sin 3x) = 0cos2 x + sin2 x = 1⇒ cos2x = 1 - sin2 x⇒ -2 cos2 3x - 3 sin 3x = -2(1 - sin2 3x) - 3 sin 3x = 0⇒ 2 sin2 3x - 3 sin 3x - 2 = 0⇒ (2 sin 3x + 1)(sin 3x - 2) = 0⇒ sin 3x = -1/2 or 2sin 3x = 2 is impossible as the range of sine is -1 ≤ sine ≤ 1Thus:sin 3x = -1/2⇒ 3x = 2nπ - π/6 or 2nπ - 5π/6⇒ x = 2/3nπ -π/18 or 2/3nπ -5π/18
Integral of tan square x secant x?
convert tan^2x into sin^2x/cos^2x and secant x into 1/cos x combine terms for integral sin^2x/cos^3x dx then sub in u= cos^3x and du=-2sin^2x dx
What is the domain of the function y sin x?
y= sin 3x
Derivative of y sin 3x 5?
The derivative of y = sin(3x + 5) is 3cos(3x + 5) but only if x is measured in radians.
Combine like terms 3x plus x?
3x + x = 4x
How do you prove that 2 sin 3x divided by sin x plus 2 cos 3x divided by cos x equals 8 cos 2x?
You need to know the trigonometric formulae for sin and cos of compound angles. sin(x+y) = sin(x)*cos(y)+cos(x)*sin(y) and cos(x+y) = cos(x)*cos(y) - sin(x)*sin(y) Using these, y = x implies that sin(2x) = sin(x+x) = 2*sin(x)cos(x) and cos(2x) = cos(x+x) = cos^2(x) - sin^2(x) Next, the triple angle formulae are: sin(3x) = sin(2x + x) = 3*sin(x) - 4*sin^3(x) and cos(3x) = 4*cos^3(x) - 3*cos(x) Then the left hand side = 2*[3*sin(x) - 4*sin^3(x)]/sin(x) + 2*[4*cos^3(x) - 3*cos(x)]/cos(x) = 6 - 8*sin^2(x) + 8cos^2(x) - 6 = 8*[cos^2(x) - sin^2(x)] = 8*cos(2x) = right hand side.
What does the sin3x equal?
sin(3x) = 3sin(x) - 4sin^3(x)
Are 3x and x like terms?
Yes, 3x and x are like terms because they have the same variable raised to the same power.
How do you solve Sin x plus sin 3x plus sin 5x plus sin 7x equals?
sin7x-sin6x+sin5x
Sin2x equals cos3x find x?
0. sin 2x = cos 3x 1. sin 2x = sin (pi/2 - 3x) [because cos u = sin (pi/2 - u)] 2. [...]
How long is each side of a 28 inch regular decagon?
It is 9.1 inches (approx). L*[sin(x) + sin(2x) + sin(3x) +sin(4x)] = 28 inches where x = 360/10 = 36 degrees. Since x = 36 deg, sin(x) = sin(4x) and sin(2x) = sin(3x) So L*[2sin(x) + 2sin(2x)] = 28 inches L*[sin(x) + sin(2x)] = 14 inches L* 1.539 = 14 approx so that L = 9.098 inches or 9.1 inches, approx.
