Answer:
72 / 3 = 24
Step-by-step explanation:
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:
Step-by-step explanation:
The domain of the function is the set of all possible inputs for the function. Therefore, the set of all possible inputs is .
Step-by-step explanation:
Create a single fraction in the numerator and denominator.
Apply the division rule of fractions by multiplying the numerator by the reciprocal or inverse of the denominator.
Simplify, if necessary.
Answer:
x = 13 ,y = 60
Step-by-step explanation:
Solve the following system:
{2 x + 6 y = 386 | (equation 1)
4 x + 4 y = 292 | (equation 2)
Swap equation 1 with equation 2:
{4 x + 4 y = 292 | (equation 1)
2 x + 6 y = 386 | (equation 2)
Subtract 1/2 × (equation 1) from equation 2:
{4 x + 4 y = 292 | (equation 1)
0 x+4 y = 240 | (equation 2)
Divide equation 1 by 4:
{x + y = 73 | (equation 1)
0 x+4 y = 240 | (equation 2)
Divide equation 2 by 4:
{x + y = 73 | (equation 1)
0 x+y = 60 | (equation 2)
Subtract equation 2 from equation 1:
{x+0 y = 13 | (equation 1)
0 x+y = 60 | (equation 2)
Collect results:
Answer: {x = 13 ,y = 60
