Find the equation of tangent line

In summary, to find the equation of the tangent line at t=0 for the given functions x=2sint and y=tant, you will need to find the gradient at t=0 by using the chain rule. Then, find a point on the line by finding the values of x and y when t=0. Finally, use the point and gradient to write the equation of the tangent line.
  • #1
th3plan
93
0

Homework Statement



Find equation of the tangent line at t=0

x=2sint
y=tant




The Attempt at a Solution



Really don't know where to start, can someone give me the hint, don't solve it, i want to try it, just need a hint
 
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  • #2
To find the equation of any line,you need a point on the line and the gradient on the line.

To find the gradient at t=0,you'll need to find dy/dx (chain rule is helpful here)

and you'll need a point on the line, you want at t=0 ,so can you find the point on the line,(x,y) when t=0?
 
  • #3
dy/dx=(dy/dt)/(dx/dt). Then go with rock.freak667's advice.
 

1. What is the equation of a tangent line?

The equation of a tangent line is a linear function that touches a curve at a specific point and has the same slope as the curve at that point.

2. How do you find the equation of a tangent line?

To find the equation of a tangent line, you need to first find the slope of the curve at the specific point. Then, you can use the point-slope form of a line to plug in the slope and the coordinates of the point to find the equation of the tangent line.

3. Can the equation of a tangent line be negative?

Yes, the equation of a tangent line can be negative. The slope of the tangent line can be positive, negative, or zero, depending on the slope of the curve at the specific point.

4. What information do I need to find the equation of a tangent line?

To find the equation of a tangent line, you need to know the coordinates of the point where the tangent line touches the curve. You also need to know the slope of the curve at that point.

5. Why is finding the equation of a tangent line important?

Finding the equation of a tangent line is important because it allows us to understand the behavior of a curve at a specific point. It also helps us to approximate the curve and make predictions about its behavior near the point of tangency.

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