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Approximation of sin x by x?
the value of sin(x) lies between -1 to +1. the approx value of sin(x)/x = 1 when x tends to 0 & sin(x)/x = 0 when x tends to infinity.
What is the period of y equals sin x?
The period is the length of x over which the equation repeats itself. In this case, y=sin x delivers y=0 at x=0 at a gradient of 1. y next equals 0 when x equals pi, but at this point the gradient is minus 1. y next equals 0 when x equals 2pi, and at this point the gradient is 1 again. Therefore the period of y=sinx is 2pi.
An ordered pair that has a y value of 0 will be located on the?
y-axis
Why does x equal 0 when finding the sin of 90 degrees?
On the unit circle sin(90) degrees is at Y = 1 and as that is on the Y axis X will equal = 0. Ask yourself. Where would 90 degrees be on a 360 degree circle? Straight up.
If x is obtuse and sin x equals b how do you show sin 2x is less than b?
you need to explain it better but with what i got i if sin x equals b obviously sin 2x is double of b hence sin 2x is more than b. {Not obvious at all, actually. And the above is false. Sin(Pi/2) = 1 and Sin(Pi)=0. But clearly 2 is not greater than 0. Contradiction.} Obtuse means Pi/2 < x < Pi So, sin(x) = b means b>0, because sin(y) > 0 if 0<y<Pi sin(2x)=2sin(x)cos(x) cos(x) < 0 because cos(Pi/2)= 0 and the derivative is negative there. Hence, sin(2x) = 2 sin(x) cos(x) = 2*b*(-K), where K is a positive constant Since b>0, -2Kb < b
Y equals 4 sin x for x equals pi?
sin(pi) = 0 so 4*sin(pi) = 0 so Y = 0
The function y equals sin θ is not a function beacause sin 30 equals sin 150?
Y=sin X is a function because for each value of X, there is exactly one Y value.
Find the value of y if sin y equals cos 48?
y = arcsin( cos 48 ); arcsin may be seen as sin-1 on your calculator.
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)
How do you solve 2 cos squared x plus sin x-1?
1
How do you find the amplitude maximum minimum and period for y equals -1 plus 3sin4x?
y = -1 + 3 sin 4xLet's look at the equation of y = 3 sin 4x, which is of the form y = A sin Bx, wherethe amplitude = |A|, and the period = (2pi)/B.So that the amplitude of the graph of y = 3 sin 4x is |3| = 3, which tell us that the maximum value of y is 3 and the minimum value is -3, and the period is (2pi)/4 = pi/2, which tell us that each cycle is completed in pi/2 radians.The graph of y = -1 + 3 sin 4x has the same amplitude and period as y = 3 sin 4x, and translates the graph of y = 3 sin 4x one unit down, so that the maximum value of y becomes 2 and the minimum value becomes -4.
When are y equals sin x and y equals cos x times cos x equal?
y=sin x y=cos x cos x sin x = cos^2 x sin x = 1-sin^2 x sin x -1 + sin^2 x = 0 sin^2 x + sin x -1 = 0 Let y=sin x y^2+y-1 = 0 This equation is of form ay^2+by+c=0 a = 1 b = 1 c = -1 y=[-b+/-sqrt(b^2-4ac)]/2a] y=[-1 +/-sqrt(1^2-4(1)(-1)]/(2)(1) discriminant is b^2-4ac =5 y=[-1 +√(5)] / 2 y=[-1 -√(5)] / 2 sin x = [-1 +√(5)] / 2 x = sin^-1 [-1 +√(5)] / 2] = 0.6662394 radians x = sin^-1 [-1 -√(5)] / 2] = sin^-1 (-1.618) -- has no solution When x = 0.6662394 radians, sin x and cos x times cos x are equal.
How do you graph sin squared x?
The graph of the function y = (sin x)^2 has the same amplitude 1, and the same period 2pi, as the graph of the function y = sin x. The only difference between them is that the part of the graph of y = sin x which is below the x-axis is reflected above x axis. In order to graph the function y = (sin x)^2, we need to find the values of (x, y) for the five key points, where 0 ≤ x ≤ 2pi. Values of (x, y) on y = (sin x)^2: x = 0, y = 0 x = pi/2, y = 1 x = pi, y = 0 x = 3pi/2, y = 1 x = 2pi, y = 0 Plot these five key points and connect them with a smooth curve and graph one complete cycle of the given function.
What is the value of x when y is 0?
if x:=x(y) then y=0 => x=x(0)
What is the sine of 180?
The sine of 180 degrees is 0. Remember, the sine value on a unit circle is the y-value. If you find f(pi) in the function f(x)=sin(x), you will get zero as an answer.
Verify sin squared x minus sin squared y equals sin x plus y times sin x-y?
To verify sin2x - sin2y = sin x + y sin (x-y) [if I've read your equation correctly] is impossible (for all x and y). A counter example can be easily found whereby the values of the two halves of the (supposed) equality are different. Let x = π and y = π/2. Then: Left hand side: sin2x - sin2y = sin2π - sin2 π/2= 0 - 12 = -1 Right hand side: sin x + y sin (x-y) = sin π + π/2 sin (π - π/2) = 0 - π/2 sin (π/2) = -π/2 Thus sin2x - sin2y = -1 ≠ -π/2 = sin x + y sin (x-y) when x = π and y = π/2, so the equality cannot be verified -
Approximation of sin x by x?
the value of sin(x) lies between -1 to +1. the approx value of sin(x)/x = 1 when x tends to 0 & sin(x)/x = 0 when x tends to infinity.
