What is the rule for a counterclockwise rotation about the origin of 210°

Mathematics

1 answer:

Phoenix [80]3 years ago

8 0

Answer:

(x, y) ⇒ (-x√3/2 +y/2, -x/2 -y√3/2)

Step-by-step explanation:

The rule for CCW rotation through an angle α is ...

(x, y) ⇒ (x·cos(α) -y·sin(α), x·sin(α) +y·cos(α))

So, for α = 210°, the rule becomes ...

(x, y) ⇒ (-x√3/2 +y/2, -x/2 -y√3/2)

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Limit question: lim x-->pi ((e^sinx)-1)/(x-pi)

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$\displaystyle\lim_{x\to\pi}\dfrac{e^{\sin x}-1}{x-\pi}$

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So the value of this limit is exactly the value of the derivative of $f(x)=e^{\sin x}$ at $x=\pi$ .

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