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vova2212 [387]
3 years ago
14

How do you find the sine and tangent of an angle if you are given the cosine?

Mathematics
1 answer:
Anni [7]3 years ago
6 0

Answer:

  • sin = √(1 -cos²)
  • tan = (√(1 -cos²))/cos

Step-by-step explanation:

\displaystyle\sin^2{\theta}+\cos^2{\theta}=1 \qquad\text{Pythagorean identiy}\\\\\sin{\theta}=\sqrt{1-\cos^2{\theta}} \qquad\text{solved for sine}\\\\\tan{\theta}=\frac{\sin{\theta}}{\cos{\theta}}=\frac{\sqrt{1-\cos^2{\theta}}}{\cos{\theta}}

_____

If you draw a triangle with a hypotenuse of 1 and an "adjacent" leg of "cos", then using the Pythagorean theorem, you can see that the "opposite" leg will be √(1-cos²) and the tangent will be (√(1-cos²))/cos. Whether or not you're allowed to draw such a triangle on paper, you can certainly do it in your mind.

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