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11 grade maths others

How do you find the exact value of cos 54?

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10 Months agoGrade
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1 Answer

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ApprovedApproved Tutor Answer10 Months ago

To find the exact value of cos 54 degrees, we can use the relationship between angles in trigonometry and some known values.

Using the Cosine of Related Angles

First, we can relate cos 54° to cos 36° using the identity:

  • cos(90° - θ) = sin(θ)

So, we have:

  • cos 54° = sin 36°

Finding sin 36°

Next, we can find sin 36° using the known value:

  • sin 36° = (√5 - 1) / 4

Thus, substituting this into our earlier equation gives:

  • cos 54° = (√5 - 1) / 4

Final Result

Therefore, the exact value of cos 54 degrees is:

cos 54° = (√5 - 1) / 4

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