If sin(8°) is known, what are the values of cos(8°) and tan(8°)?

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To find the values of cos(8°) and tan(8°) given sin(8°), we can use some basic trigonometric identities and calculations.

First, we know the Pythagorean identity which states:

sin²(θ) + cos²(θ) = 1

Using this identity, we can rearrange it to find cos(8°):

cos(θ) = √(1 – sin²(θ))

If sin(8°) is given as approximately 0.13917 (this is a known value), we can calculate cos(8°):

cos(8°) = √(1 - sin²(8°))

= √(1 - (0.13917)²)

= √(1 - 0.0194)

= √(0.9806)

≈ 0.9903

Now that we have the value of cos(8°), we can find tan(8°) using the relationship:

tan(θ) = sin(θ) / cos(θ)

tan(8°) = sin(8°) / cos(8°)

= 0.13917 / 0.9903

≈ 0.1401

So, the values are:

  • cos(8°) ≈ 0.9903
  • tan(8°) ≈ 0.1401

This shows how trigonometric identities can help us find values from one known trigonometric function, making it easier to understand and calculate the relationships between sine, cosine, and tangent!

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