Assuming that arcs are given in degrees, call S the following sum:
S = sin 1° + sin 2° + sin 3° + ... + sin 359° + sin 360°
Rearranging the terms, you can rewrite S as
S = [sin 1° + sin 359°] + [sin 2° + sin 358°] + ... + [sin 179° + sin 181°] + sin 180° +
+ sin 360°
S = [sin 1° + sin(360° – 1°)] + [sin 2° + sin(360° – 2°)] + ...+ [sin 179° + sin(360° – 179)°]
+ sin 180° + sin 360° (i)
But for any real k,
sin(360° – k) = – sin k
then,
S = [sin 1° – sin 1°] + [sin 2° – sin 2°] + ... + [sin 179° – sin 179°] + sin 180° + sin 360°
S = 0 + 0 + ... + 0 + 0 + 0 (... as sin 180° = sin 360° = 0)
S = 0
Each pair of terms in brackets cancel out themselves, so the sum equals zero.
∴ sin 1° + sin 2° + sin 3° + ... + sin 359° + sin 360° = 0 ✔
I hope this helps. =)
Tags: <em>sum summatory trigonometric trig function sine sin trigonometry</em>
Answer:
The correct option is;
After 64 seconds, ABOUT HALF of the brands of milk chocolate ARE LIKELY to melt, and NONE of the brands of dark chocolate ARE LIKELY to melt
Step-by-step explanation:
Here we have for the milk chocolate
Min = 29 s
Lower quartile Q₁ = 44 s
Median = 64 s
Upper quartile Q₂ = 93 s
Max = 129 s
For the dark chocolate
Min = 210 s
Lower quartile Q₁ = 237 s
Median = 259 s
Upper quartile Q₂ = 295 s
Max = 320 s
As seen from the values of the box plot, after the median time of 64 seconds which represents half of the test results of the milk chocolate about half of the brands of milk chocolate are likely to melt, while the dark brands only start to melt after 210 seconds.
Therefore the correct option is
After 64 seconds, ABOUT HALF of the brands of milk chocolate ARE LIKELY to melt, and NONE of the brands of dark chocolate ARE LIKELY to melt.
Answer:
14
Step-by-step explanation:
21-3^2+2
3 to the second power is 9
then, 21 - 9 + 2
left to right.....
21 - 9 = 12
12+2=14
