# What is the slope of the tangent line of #secx-cscy= C #, where C is an arbitrary constant, at #(pi/3,pi/3)#?

Graph, with tangent: graph{(1/cos x- 1/ sin y - 2 ( 1- 1/3 sqrt3 ))(y-1/3pi+3sqrt3(x-1/3pi))(y-1/3pi-3sqrt3(x+1/3pi))((x-1/3pi)^2+(y-1/3pi)^2-0.025)((x+1/3pi)^2+(y-1/3pi)^2-0.025)=0}

Indeed, vivid.

Did you observe that I have shown also

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

To find the slope of the tangent line at the point ((\frac{\pi}{3}, \frac{\pi}{3})), we need to find the derivative of the given function with respect to (x) and (y), and then evaluate it at that point.

Given equation: (\sec(x) - \csc(y) = C)

Taking partial derivatives with respect to (x) and (y), we get:

(\frac{\partial}{\partial x}(\sec(x) - \csc(y)) = \frac{\partial}{\partial x}(C))

(\frac{\partial}{\partial y}(\sec(x) - \csc(y)) = \frac{\partial}{\partial y}(C))

To compute these partial derivatives, we use the following identities:

(\frac{d}{dx} \sec(x) = \sec(x) \tan(x))

(\frac{d}{dy} \csc(y) = -\csc(y) \cot(y))

Substituting these derivatives into the partial derivatives, we have:

(\sec(x) \tan(x) = 0)

(-\csc(y) \cot(y) = 0)

Solving these equations gives us (x = \frac{\pi}{2}) and (y = \frac{\pi}{2}).

So, at the point ((\frac{\pi}{3}, \frac{\pi}{3})), the slope of the tangent line is undefined.

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

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- How do you implicitly differentiate # x^2+x/y-xy^2+x=3y #?
- What is the derivative of #x/(1+x^2)#?
- How do I find the derivative of #y=ln(secx + tanx)#?
- How do you differentiate #sqrt(cos(x^2+2))+sqrt(cos^2x+2)#?
- How do you find the slope of the tangent line to the curve #6x^2 - 2xy + 3y^3 = 216# at the point 6,0?

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