What is the value of sin 42 π ?

Question

What is the value of sin 42 &#960; ?

Accepted Answer

Choice A is correct. The sine of a number t is the y -coordinate of the point arrived at by traveling a distance of t units counterclockwise around the unit circle from the starting point 1 , 0 . Since the unit circle has a circumference of 2 &pi; units, it follows that one full rotation around the circle is equal to a distance of 2 &pi; units. Therefore, a distance of 42 &pi; units around the circle from the starting point 1 , 0 would result in exactly 21 full rotations, arriving back at the point 1 , 0 . So, sin 42 &pi; is equal to the y -coordinate of the point 1 , 0 , which is 0 . Choice B is incorrect and may result from conceptual or calculation errors. Choice C is incorrect and may result from conceptual or calculation errors. Choice D is incorrect. This is the value of cos 42 &pi; , not sin 42 &pi; .

Question 8440c7