Question

How do you find the equation of the line tangent to `y=cosx` at x=π/4?

Answer 1

`y-1/\sqrt{2}=(-1)/\sqrt{2}(x-\pi/4)`

Explanation:

Given that to find the equation of a tangent, we first need to find the slope(`m`) of the equation. The given slope of the equation can be found by differentiating the function, and then substituting the value of either `x` or `y` in the differentiated function.

So here(assuming you know what the derivative of cos function is), `y=cos(x)`.
From the above paragraph, you'll understand that `m=\frac{d}{dx}(f(x))`
`f(x)=y=cos(x)`
`:. \frac{d}{dx}(y)=-sin(x)`
The given slope for the tangent should be found at `x=\pi/4`
So, `\frac{d}{dx}(y)|_(x=\pi/4)=-sin(\pi/4)=-1/\sqrt{2}`

Now, the given slope equation is
`y-y_o=m(x-x_o)`
See that we need to find `y_o` and `x_o`
From the given equation main we can find that out that at `x_o=\pi/4` `y_o=1/\sqrt{2}`
So, finally, the answer is as provided above.