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Why does cos negative theta equals positive theta?
You must think of the unit circle. negative theta is in either radians or degrees and represents a specific area on the unit circle. Remember the unit circle is also like a coordinate plane and cos is the x while sin is the y coordinate. Here is an example: cos(-45): The cos of negative 45 degrees is pi/4 and cos(45) is also pi/4
What is the derivative of sin pi x?
If you mean y = Sin(pi(x)) Then Use the chain rule dy/dx = dy/du X du/dx Let pi(x) = u y = Sin (u) dy/du = Cos(u) u = pi(x) du/dx = pi Combining dy/dx = pi Cos(u) = piCos (pi(x)). The answer!!!!!
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.
If tan y equals to x where y is acute find 3 cos y in terms of x?
3cos(y) = 3/(sqrt(1+x^2)
How do you find conjugate of cos z?
To find the conjugate of ( \cos z ) for a complex number ( z = x + iy ) (where ( x ) and ( y ) are real numbers), you can use the formula for the cosine of a complex argument: [ \cos z = \cos(x + iy) = \cos x \cosh y - i \sin x \sinh y. ] The conjugate of ( \cos z ) is obtained by taking the complex conjugate of the expression, resulting in: [ \overline{\cos z} = \cos x \cosh y + i \sin x \sinh y. ]
What is the derivative of cos pi x plus sin pi y all to the 8th power equals 44?
(cos(pi x) + sin(pi y) )^8 = 44 differentiate both sides with respect to x 8 ( cos(pi x) + sin (pi y ) )^7 d/dx ( cos(pi x) + sin (pi y) = 0 8 ( cos(pi x) + sin (pi y ) )^7 (-sin (pi x) pi + cos (pi y) pi dy/dx ) = 0 8 ( cos(pi x) + sin (pi y ) )^7 (pi cos(pi y) dy/dx - pi sin (pi x) ) = 0 cos(pi y) dy/dx - pi sin(pi x) = 0 cos(pi y) dy/dx = sin(pi x) dy/dx = sin (pi x) / cos(pi y)
Find the equation of the line tangent to the graph of y equals cos2x at x equals pi divided by 4?
0.5
What is x equals y squared over co sign times pi?
Either you mean "cos(x) multiplied by pi", (i.e pi*cos(x)) or "cos(pi)" (i.e cosine of pi), but it is unclear which you mean from the question. Please clarify.
What is the equation of the line tangent to the curve y equals cos x at the point x equals pi over 6?
y = 2(x) - (pi/3) + (sqrt(3)/2)
Y equals 4 sin x for x equals pi?
sin(pi) = 0 so 4*sin(pi) = 0 so Y = 0
What is the range of y equals arc cos x?
It is pi radians wide. The end point is arbitrary.
What is x equal y sq over cos x pi?
Can you please claify if you mean x=y^2/ pi*cos(x) , or x=y^2/cos(pi), since they are very different sums.
What is the range for y equals 4 cos parantheses2xparantheses?
The range for y = 4 cos (2x) is [-4, +4].Not asked, but answered for completeness sake, the domain is [-infinity, +infinity].
Why does cos negative theta equals positive theta?
You must think of the unit circle. negative theta is in either radians or degrees and represents a specific area on the unit circle. Remember the unit circle is also like a coordinate plane and cos is the x while sin is the y coordinate. Here is an example: cos(-45): The cos of negative 45 degrees is pi/4 and cos(45) is also pi/4
If Sin equals x and Cos equals y then x squared equals what function of y?
If x = sin θ and y = cos θ then: sin² θ + cos² θ = 1 → x² + y² = 1 → x² = 1 - y²
How do you solve cos squared x - cosx equals 2 for 0x2pi?
cos2(x) - cos(x) = 2 Let y = cos(x) then y2 - y = 2 or y2 - y - 2 = 0 factorising, (y - 2)(y + 1) = 0 that is y = 2 or y = -1 Substitutng back, this would require cos(x) = 2 or cos(x) = -1 But cos(x) cannot be 2 so cos(x) = -1 Then x = cos-1(-1) => x = pi radians.
What is sin23A minus sin7A upon sin2A plus sin14A if A equals pi upon 21?
Using the identity, sin(X)+sin(Y) = 2*sin[(x+y)/2]*cos[(x-y)/2] the expression becomes {2*sin[(23A-7A)/2]*cos[(23A+7A)/2]}/{2*sin[(2A+14A)/2]*cos[(2A-14A)/2]} = {2*sin(8A)*cos(15A)}/{2*sin(8A)*cos(-6A)} = cos(15A)/cos(-6A)} = cos(15A)/cos(6A)} since cos(-x) = cos(x) When A = pi/21, 15A = 15*pi/21 and 6A = 6*pi/21 = pi - 15pi/21 Therefore, cos(6A) = - cos(15A) and hence the expression = -1.
