A fox sees a rabbit 35 feet away and starts chasing it. As soon as the fox starts moving the rabbit sees it and starts running a

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

$9.62, Mindy has to reimburse Nora.

Given: AD ≅ BC and AD ∥ BC

Prove: ABCD is a parallelogram.

Statements                                                                 Reasons

 1. AD ≅ BC; AD ∥ BC                                                1. provided

 2. ∠CAD and ∠ACB are alternate interior angles        2. definition of alternate interior angles

3. ∠CAD ≅ ∠ACB                                                    3. congruence of alternate interior angles

4. AC ≅ AC                                                              4. reflexive property

 5. △CAD ≅ △ACB                                                  5. SAS congruency theorem

6. AB ≅ CD                                                            6. Congruent triangles have congruent corresponding parts (CPCTC)

7. ABCD is a parallelogram                                  7. theorem for sides of parallelograms

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Answer: D. 45 inches, 75 inches

Step-by-step explanation:

To resolve this inquiry, we first need to divide the board's total length by the number of segments forming the two sections.

Given the ratio of 3:5, one section consists of 3 segments and the other of 5, making a total of 8 segments.

120 divided by 8 equals 15 inches for each segment.

Next, we multiply the length of each segment by how many segments each section has (3 and 5).

15 times 3 equals 45 inches.

15 times 5 equals 75 inches.

Answer:

40 * x - 600 = 0

Step-by-step explanation:

Initially, identify the variable (x) in the equation, representing the number of days it takes Leilah to review her flashcards. To study 600 out of her 2400 cards, having gone through 1800 already, we arrive at:

2400 - 1800 = 40 * x

rearranging leads to

40 * x - 600 = 0

This equation describes the situation above