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:
Which of the following best states why the Battle of Antietam was considered a turning point in the war?
Step-by-step explanation:
im smart∈∉∧¬∠⇅khvycgufykxd
Multiply the area of the circle by the percentage:
60 square units x 50% = 60 x 0.50 = 30
50% 0f the circle id 30 square units.
So what is given is:
length = 1.9 * w, you want to convert this to w = ...
This is done by dividing left and right by 1.9, so you get:
length/1.9 = 1.9*w/1.9, which simplifies to w = length/1.9
Another approach is to replace the multiplication with a simpler one in your head. So in stead of reading "length = 1.9 * width, what is width?", you read "6 = 2*3, what is 3?". You'll immediately realize 3 = 6/2, and that shows you how to change the real equation, ie., width = length/1.9.
