Question

How to find the value of sin 450 degrees and sin 56 degrees without using a calculator and table? A) For sin 450 degrees, use the identity sin(450) = sin(360 + 90) = sin(90) = 1. For sin 56 degrees, estimate it to be between 0 and 1. B) For sin 450 degrees, use the identity sin(450) = sin(360 + 90) = sin(90) = 0. For sin 56 degrees, estimate it to be between 0 and 1. C) For sin 450 degrees, use the identity sin(450) = sin(360 + 90) = sin(90) = 1. For sin 56 degrees, estimate it to be between -1 and 1. D) For sin 450 degrees, use the identity sin(450) = sin(360 + 90) = sin(90) = 0. For sin 56 degrees, estimate it to be between -1 and 1.

Answer 1

Firstly, recall that sine is a periodic function with a period of 360 degrees. This means if you add or subtract 360 degrees from any angle, the sine of the resulting angle remains the same.

So, to find the sine of 450 degrees, we can subtract 360 from 450 to get an equivalent angle. Hence, 450 degrees is the same as 90 degrees (450 - 360 = 90 degrees). The sine of 90 degrees is 1.

Therefore, sin(450 degrees) is equal to 1.

Next let's look at sin(56 degrees). The sine function outputs values between -1 and 1 for any given inputs. For angles between 0 and 90 degrees, sine values are always between 0 and 1.

Hence, sin(56 degrees) must be between 0 and 1.

Combing these two pieces of information, the only option that fits the computation is option A: sin(450 degrees) is 1 and sin(56 degrees) is estimated to be between 0 and 1.

Answer: A) For sin 450 degrees, use the identity sin(450) = sin(360 + 90) = sin(90) = 1. For sin 56 degrees, estimate it to be between 0 and 1.