Video: Calculating the Sine Function of a Given Angle

Calculate sin 75°4′12″ giving the answer to four decimal places.

01:26

Video Transcript

Calculate the sin of 75 degrees, four minutes, 12 seconds, giving the answer to four decimal places.

We know that one degree is equal to 60 minutes, which is equal to 3600 seconds. Decimal degrees are in the form the degree plus the minutes out of 60 plus the seconds out of 3600. And we have the sin of 75 degrees, four minutes, and 12 seconds. So let’s begin simplifying.

75 degrees is simply 75. And then four divided by 60 is equal to 0.06666. And 12 divided by 3600 is equal to 0.00333. So adding these numbers together inside the parentheses, we now have the sin of 75.06999. So plugging this into our calculator, we will find that it’s equal to 0.96624.

But we need to round four decimal places. So we will either keep the two a two or round it up to a three. So we look at the number to the right of it. And since four is less than five, we will keep the two a two. Therefore, our final answer will be 0.9662.

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