A teacher surveys 30 students on the number of books they read over the summer. The data

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

Hello! I'm here to assist you! To calculate interest, we apply the formula prt, which involves multiplying the principal (the amount of money initially), the rate (the interest rate), and the time (typically in years). Here are the results:

$252 at 8% over 2 years yields $40.32
$400 at 2% for a duration of 6 months results in $4
$5,000 at 3.5% for 1 year gives $175
$6,240 at 10% for 9 months amounts to $468

For period calculations, we convert months into decimals: 6 months equals 0.5 years, and 9 months equals 0.75 years. Simply multiply the principal amount by the percentage in decimal form and by the time, and that’s it!

Answer:

I believe it's 2.

Step-by-step explanation:

10, and -10

First, you would divide 127 by 8 and then multiply the result by three uniforms for each employee.

This is a useful question to answer. I believe there’s not a single place on earth that is free from some form of tax.

Tax is applicable only during transactions where money is exchanged, and it does not affect discounts.

If you decide to take the offer, the cost is determined by:

Cost for two pizzas = standard price - discount applied.

Cost for two pizzas = 2*10.50 - 2.00

Cost for two pizzas = 21 - 2

Cost for two pizzas = 19.00 dollars.

Now, you should add the sales tax to this amount. There are two methods to do this: the detailed method or the quicker method.

Detailed Method

Calculate the sales tax:

Tax = rate * total cost

Tax = (7.5/100) * 19

Tax = 1.425, don’t round yet.

Total Amount = total purchase + tax

Total Amount = 19.00 + 1.425 = 20.425. Now, round it off. The way to round when the last digit is 5 can vary; I usually round up, so my final answer would be 20.43 <<<<< This is the answer.

Quick Method

Final Cost = (Original Price - discount)*(1 + tax rate/100)

Final Cost = (21 - 2)*(1 + 7.5/100)

Final Cost = 19 * (1.075)

Final Cost = 20.425, which rounds to 20.43.