NOTES:
y = sin x
x | y
-2π | 0
[tex]-\frac{3\pi}{2}[/tex] | 1
-π | 0
[tex]-\frac{\pi}{2}[/tex] | -1
0 | 0
[tex]\frac{\pi}{2}[/tex] | 1
π | 0
[tex]\frac{3\pi}{2}[/tex] | -1
2π | 0
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Graph: B
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1) NO
Even function is when f(x) = f(-x)
Check: sin (x) = sin (-x)
Let x = [tex]\frac{\pi}{2}[/tex]
sin ([tex]\frac{\pi}{2}[/tex]) = 1
sin ([tex]-\frac{\pi}{2}[/tex]) = -1
f(x) ≠ f(-x) so sin (x) is not an even function
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2) YES
sin (-2π) = 0
sin ([tex]-\frac{3\pi}{2}[/tex]) = 1
0 → 1 is "increasing"
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3) YES
There are no restrictions on x so the domain is x = All Real Numbers
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4) YES
y = sin (x) has the coordinate (0, 0) so the y-intercept is 0
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5) NO
Let n = 0, then [tex]\frac{2(0) + 1}{2}\pi[/tex]
= [tex]\frac{\pi}{2}[/tex]
sin ([tex]\frac{\pi}{2}[/tex]) = 1 so it is not a zero
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6) NO
Let n = 0, then x = 0π
= 0
This is a zero, not a minimum. Minimums are when y = -1.
