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guapka [62]
3 years ago
9

If cos(x)=1/4 what is sin(x) and tan(x)

Mathematics
1 answer:
anygoal [31]3 years ago
3 0
You can use the identity
  cos(x)² +sin(x)² = 1
to find sin(x) from cos(x) or vice versa.

  (1/4)² +sin(x)² = 1
  sin(x)² = 1 - 1/16
  sin(x) = ±(√15)/4


Then the tangent can be computed as the ratio of sine to cosine.
  tan(x) = sin(x)/cos(x) = (±(√15)/4)/(1/4)
  tan(x) = ±√15


There are two possible answers.
In the first quadrant:
  sin(x) = (√15)/4
  tan(x) = √15

In the fourth quadrant:
  sin(x) = -(√15)/4
  tan(x) = -√15
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