How do you find the equation of the line tangent to y=cos⁡x at x=π4?

Question

Dallelopeelvep2yc · Accepted Answer

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}{d x} (f (x))

f (x) = y = \cos (x)

∴ \frac{d}{d x} (y) = - \sin (x)

The given slope for the tangent should be found at

x = \frac{π}{4}

So,

\frac{d}{d x} (y) ∣_{x = \frac{π}{4}} = - \sin (\frac{π}{4}) = - \frac{1}{\sqrt{2}}

Now, the given slope equation is

y - y_{0} = m (x - x_{0})

See that we need to find

y_{0}

and

x_{0}

From the given equation main we can find that out that at

x_{0} = \frac{π}{4} y_{0} = \frac{1}{\sqrt{2}}

So, finally, the answer is as provided above.

How do you find the equation of the

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