Which of the following is the best linear approximation for f(x) = sin(x) near x = π seconds?

y = -x + π - 1
y = -1
y = -x + π
y = -x - π

Question

Which of the following is the best linear approximation for f(x) = sin(x) near x = π seconds? 
 	
	y = -x + π - 1
	y = -1
	y = -x + π
	y = -x - π

zepdrix · Answer

Hmm I don't think you need to do anything fancy here.
Just think about the `actual value` of sin(x) at x=pi,
and see which options gets you closest to that value.

zepdrix · Answer

$$\large\rm \sin(\pi)=?$$

anonymous · Answer

@zepdrix is right. TIP: It's equally beneficial to glance at a sine wave on a graph.

anonymous · Answer

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anonymous · Answer

For a more systematic way (assuming you know calculus), the linear approximation of a function at a point is:

$L = f(x_{0}) + f'(x_{0})(x-x_{0})$

Then just throw everything into that formula. 

$\large \sin(\pi) = ?$

$\large \frac{d}{dx}\sin(x) \rvert_{x=\pi} =  ?$

chris215 · Answer

-1?

zepdrix · Answer

$\large\rm \sin(\pi)\ne-1$

chris215 · Answer

ok so does that mean the answer is y=-1?