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:
3.844 x 10^5
3.844E-5
3.844 × 10-5 kilometers
Step-by-step explanation:
Answer:
Step-by-step explanation:
It would be greatly appreciated if you gave me the brainlest
To evaluate the expression given above, we just have to substitute the values assigned to each variable in the expression. The expression would be:
<span>6j23kl−3
We evaluate as follows:
</span><span>6j 23 kl−3
6(3)(23)(7)(33) - 3
95631
Hope this answers the question. Have a nice day.
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5 would be the right answer.
