WEBVTT
00:00:00.840 --> 00:00:10.230
Find sin π given 51 cos 90 degrees minus π is equal to 24, where π is a positive acute angle.
00:00:11.530 --> 00:00:20.570
This is a question about cofunction identities, and one in particular thatβs cos of 90 degrees minus π is equal to sin π.
00:00:21.880 --> 00:00:25.300
You can see that this identity is true by taking a right triangle.
00:00:26.440 --> 00:00:37.470
If this angle has measure π, then as the sum of the measures of the angles in a triangle is equal to 180 degrees, the other angle must be 90 degrees minus π.
00:00:39.020 --> 00:00:45.620
Sin π is equal to the length of the side opposite the angle, divided by the length of the hypotenuse.
00:00:46.630 --> 00:00:50.150
Okay and what about cos of 90 degrees minus π?
00:00:51.490 --> 00:00:58.730
Well thatβs equal to the length of the side adjacent to that angle, divided by the length of the hypotenuse.
00:01:00.070 --> 00:01:09.880
And so using this right triangle, we can see that sin π and cos 90 degrees minus π are the same ratio of sides, and so they are equal.
00:01:11.770 --> 00:01:16.040
This means that we can replace cos of 90 degrees minus π by sin π.
00:01:17.450 --> 00:01:20.960
So we get 51 sin π is equal to 24.
00:01:22.180 --> 00:01:27.140
Dividing both sides by 51, we get that sin π is equal to 24 over 51.
00:01:28.420 --> 00:01:36.960
And we can simplify our fraction by dividing both numerator and denominator by three to get that sin π is equal to eight over 17.