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
Answer:
45 mph
Step-by-step explanation:
Calculate the unit rate (i.e., speed):
6 mi 60 min
--------- * ------------- = (3/4)(60) mph = 45 mph
8 min 1 hr
Every confidence interval correlates with a specific z value. As the confidence interval expands, so does the corresponding z value.
You can compute the confidence interval using the formula:
Here
represents the mean, z is the respective z value, s denotes the standard deviation, and n indicates the sample size.
Standard deviation is simply the square root of variance:
For a confidence interval of 95%, the z value is <span>1.960.
</span>Now, we can compute the confidence interval for our income:
Answer: I require the answer as well. I'm hoping someone responds
Step-by-step guidance:
To solve simple equations like this, it's essential to apply the order of operations defined by PEMDAS. This acronym represents the sequential operations needed for solving equations.
PEMDAS indicates Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction.
According to PEMDAS, multiplication takes precedence over addition, leading us to:
5 + [1*10] = 5 + 10 = 15.
