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topjm [15]
2 years ago
7

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

Mathematics
1 answer:
MArishka [77]2 years ago
6 0
<h3>Answer:  cos(76)</h3>

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

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.

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