Find the value of sin 301.8° rounded to four significant digits.
A) -1.1199
B) -0.4449
C) -1.1749
D) 0
E) -0.8499

Question

Quizplus · Accepted Answer

To find the value of sin(301.8°), we first need to convert it to an angle between 0° and 360°, since sine is a periodic function with a period of 360°.

301.8° is greater than 360°, so we can subtract 360° from it to get an equivalent angle between 0° and 360°:

301.8° - 360° = -58.2°

Since sine is negative in the third and fourth quadrants of the unit circle (where the x-coordinate is negative), we can find that the sine of -58.2° is equal to the sine of 121.8°:

sin(-58.2°) = sin(121.8°)

To find the sine of 121.8°, we can use the fact that the sine function has a period of 360° and is symmetric about the line x = 180°:

sin(121.8°) = sin(121.8° - 360°) = sin(-238.2°)

Since -238.2° is equivalent to 121.8° in terms of the sine function, we can use the sine of 121.8° to approximate the sine of -58.2° and therefore the sine of 301.8°:

sin 301.8° = sin(121.8°) ≈ -0.8499 (rounded to four significant digits)

Therefore, the best choice is E.

Find the Value of Sin 301