# How do you find the x-coordinates of all points on the curve #y=sin2x-2sinx# at which the tangent line is horizontal?

In the interval

Hopefully this helps!

By signing up, you agree to our Terms of Service and Privacy Policy

To find the x-coordinates of all points on the curve y = sin(2x) - 2sin(x) at which the tangent line is horizontal, we need to find the values of x where the derivative of the function is equal to zero.

First, let's find the derivative of y with respect to x:

dy/dx = d/dx(sin(2x) - 2sin(x)) = 2cos(2x) - 2cos(x)

Next, we set the derivative equal to zero and solve for x:

2cos(2x) - 2cos(x) = 0

Now, we can simplify this equation:

cos(2x) - cos(x) = 0

Using the trigonometric identity cos(2x) = 2cos^2(x) - 1, we can rewrite the equation as:

2cos^2(x) - 1 - cos(x) = 0

Rearranging the terms:

2cos^2(x) - cos(x) - 1 = 0

Now, we can solve this quadratic equation for cos(x) using factoring, quadratic formula, or other methods. Once we find the values of cos(x), we can find the corresponding values of x by taking the inverse cosine (arccos) of each cos(x) value.

These x-values will represent the x-coordinates of all points on the curve where the tangent line is horizontal.

By signing up, you agree to our Terms of Service and Privacy Policy

To find the x-coordinates of all points on the curve ( y = \sin(2x) - 2\sin(x) ) at which the tangent line is horizontal, we need to find where the derivative of the function with respect to x is equal to zero, as the derivative gives us the slope of the tangent line.

First, let's find the derivative of the function ( y = \sin(2x) - 2\sin(x) ) with respect to x:

[ \frac{dy}{dx} = 2\cos(2x) - 2\cos(x) ]

Now, we set the derivative equal to zero and solve for x:

[ 2\cos(2x) - 2\cos(x) = 0 ]

[ \cos(2x) = \cos(x) ]

[ 2x = 2n\pi \pm x ]

[ x = n\pi ]

So, the x-coordinates of all points on the curve where the tangent line is horizontal are ( x = n\pi ), where ( n ) is any integer.

By signing up, you agree to our Terms of Service and Privacy Policy

- Tiffany has been dieting for 6 months. After 1 month Tiffany lost a total of 8 pounds. After 6 months, she lost a total of 25 pounds. How do you find the average rate of change of pounds per month?
- How do you find the equations for the tangent plane to the surface #h(x,y)=cosy# through #(5, pi/4, sqrt2/2)#?
- How do you find the slope of a tangent line to the graph of the function #y^2-2x-4y-1=0#, at (-2,1)?
- What is the equation of the line tangent to #f(x)=sin x + cos^2 x # at #x=0#?
- What is the equation of the tangent line of #f(x)=4secx–8cosx# at #x=(pi/3)#?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7