sin(pi) = 0 so 4*sin(pi) = 0 so Y = 0
(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)
The same as the period of y = sin x. This period is equal to (2 x pi).
The amplitude of the function ( y = 3 \sin(4x) ) is 3, which is the coefficient in front of the sine function. The period can be found using the formula ( \frac{2\pi}{b} ), where ( b ) is the coefficient of ( x ); in this case, ( b = 4 ). Therefore, the period is ( \frac{2\pi}{4} = \frac{\pi}{2} ).
The amplitude is 4 .
'Y' varies between -4 and +4. Viewed as a wave, its amplitude is 4.
(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)
Pi
2
The period of y=sin(x) is 2*pi, so sin(x) repeats every 2*pi units. sin(5x) repeats every 2*pi/5 units. In general, the period of y=sin(n*x) is 2*pi/n.
Pi radians (180 degrees) is.
0.5
y = sin(-x)Amplitude = 1Period = 2 pi
The same as the period of y = sin x. This period is equal to (2 x pi).
sin(theta) reach a maximum at pi / 2 + all even multiple of 2 pi. As a result, the smallest positive value of x where y = sin(2x) is maximal is pi / 2.
The amplitude is 4 .
Two thirds pi, or rather 2pi/3.
'Y' varies between -4 and +4. Viewed as a wave, its amplitude is 4.