Assuming arcs are measured in degrees, let S represent the following sum:
S = sin 1° + sin 2° + sin 3° +... + sin 359° + sin 360°
By rearranging, S can be reformulated 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)
However, for any real k,
sin(360° – k) = – sin k
Thus,
S = [sin 1° – sin 1°] + [sin 2° – sin 2°] +... + [sin 179° – sin 179°] + sin 180° + sin 360°
S results in 0 + 0 +... + 0 + 0 + 0 (... since sine of 180° and 360° are both equal to 0)
Therefore, S equals 0.
Each pair within the brackets negates itself, leading the sum to total zero.
∴ sin 1° + sin 2° + sin 3° +... + sin 359° + sin 360° equals 0. ✔
I hope this clarifies things. =)
Tags: sum summatory trigonometric trig function sine sin trigonometry
I will designate the hourly rate for weekdays as x and for weekends as y. The equations are arranged as follows:
13x + 14y = $250.90
15x + 8y = $204.70
This gives us a system of equations which can be solved by multiplying the first equation by 4 and the second by -7. This leads to:
52x + 56y = $1003.60
-105x - 56y = -$1432.90
By summing these two equations, we arrive at:
-53x = -$429.30 --> 53x = $429.30 --> (dividing both sides by 53) x = 8.10. This represents her hourly wage on weekdays.
Substituting our value for x allows us to determine y. I will utilize the first equation, but either could work.
$105.30 + 14y = $250.90. To isolate y, subtract $105.30 from both sides --> 14y = $145.60 divide by 14 --> y = $10.40
Thus, we find that her earnings are $8.10 per hour on weekdays and $10.40 per hour on weekends. The difference shows she earns $2.30 more on weekends than on weekdays.
Hey! Hi! Hola! Aloha!
When rounding 1199.28856995 to the nearest tenth, the result is 119.3.
I hope this is helpful!
Greetings
The equation is
A = p (1 + r)^t
What is the future value?
P is the present value 1020
R is the rate of increase 0.03
T is the duration 2015−2001=14 years
So
A = 1,020 × (1 + 0.03)^(14)
A = 1,542.8 rounding it gives
A = 1543
Hope this information is helpful
Response:
The height of the water when it reaches 4 inches is 
.
Detailed Explanation:
Flow rate of water from the cone = R=
Height of the cup = h = 6 inches
Radius of the cup = r = 3 inches
r = h/2
Volume of the cone = 
h = 4 inches
The height of the water when it is 4 inches deep is .
