Question Video: Using Cofunction Identities to Evaluate a Trigonometric Function | Nagwa Question Video: Using Cofunction Identities to Evaluate a Trigonometric Function | Nagwa

# Question Video: Using Cofunction Identities to Evaluate a Trigonometric Function Mathematics • First Year of Secondary School

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Find sin π given 51 cos (90Β° β π) = 24 where π is a positive acute angle.

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### Video Transcript

Find sin π given 51 cos 90 degrees minus π is equal to 24, where π is a positive acute angle.

This is a question about cofunction identities, and one in particular thatβs cos of 90 degrees minus π is equal to sin π. You can see that this identity is true by taking a right triangle.

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.

Sin π is equal to the length of the side opposite the angle, divided by the length of the hypotenuse.

Okay and what about cos of 90 degrees minus π? Well thatβs equal to the length of the side adjacent to that angle, divided by the length of the hypotenuse. 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.

This means that we can replace cos of 90 degrees minus π by sin π. So we get 51 sin π is equal to 24. Dividing both sides by 51, we get that sin π is equal to 24 over 51. 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.

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