Question

How to find the value of sin(-1200) stepwise?

A. Sin(-1200) is undefined.
B. Sin(-1200) = sin(1200)
C. Sin(-1200) = -sin(120)
D. Sin(-1200) = -sin(120)

Answer 1

The value of sin(-1200) is found by using the sine function's periodicity and the fact that sine is an odd function. By adding multiples of the function's period (360 degrees) to -1200, we find that sin(-1200) is equivalent to -sin(120), so the answer is C. Sin(-1200) = -sin(120).

Step-by-step explanation:

How to Find the Value of sin(-1200)-

The value of sin(-1200) can be found by using the properties of sine and its periodicity. The sine function has a period of 360 degrees, which means that sin(θ) = sin(θ + 360k) for any integer k. To find an equivalent angle between 0 and 360 degrees for -1200, we can add multiples of 360 until we are in that range.

1. First, divide -1200 by 360 to find how many periods of 360 are in -1200:
   -1200 ÷ 360 = -3 with a remainder of -120.
2. Add 360 degrees four times to get an equivalent positive angle:
   -120 + 360(4) = 1320 degrees.
3. To bring this within 0 to 360 degrees, divide 1320 by 360:
   1320 ÷ 360 = 3 with a remainder of 240. Therefore, sin(-1200) is equivalent to sin(240).
4. Now, we use the fact that sine is an odd function, which means sin(-θ) = -sin(θ).
   Therefore, sin(-1200) = -sin(120).

The correct answer is C. Sin(-1200) = -sin(120)