24.4k views
3 votes
Write expression as a sine or cosine of an angle.
cos 94° cos 18° + sin 94° sin 18° ​

Write expression as a sine or cosine of an angle. cos 94° cos 18° + sin 94° sin 18° ​-example-1

1 Answer

3 votes

Answer: cos(76)

=========================================================

Step-by-step explanation:

The original expression is of the pattern cos cos + sin sin. This pattern matches the second identity in the hint. Specifically, we'll say the following:

cos(A - B) = cos(A)cos(B) + sin(A)sin(B)

cos(A)cos(B) + sin(A)sin(B) = cos(A - B)

cos(94)cos(18) + sin(94)sin(18) = cos(94 - 18)

cos(94)cos(18) + sin(94)sin(18) = cos(76)

----------

We can verify this by use of a calculator. Make sure your calculator is in degree mode.

  • cos(94)cos(18) + sin(94)sin(18) = 0.24192
  • cos(76) = 0.24192

Both expressions give the same decimal approximation, so this helps confirm the two expressions are equal. You could also use the idea that if x = y, then x-y = 0. Through this method, you'll subtract the left and right hand sides and you should get (very close to) zero.

User Mellville
by
8.3k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories