Question

Find sin(2x), cos(2x), and tan(2x) from the given information. tan(x) = − 1/2 , cos(x) > 0

Answer 1

Answer:

• sin(2x) = -4/5
• cos(2x) = 3/5
• tan(2x) = -4/3

Step-by-step explanation:

It may be easiest to start with tan(2x).

  tan(2x) = 2tan(x)/(1 -tan(x)²)

  tan(2x) = 2(-1/2)/(1 -(-1/2)²) = -1/(3/4)

  tan(2x) = -4/3 . . . . . still a 4th-quadrant angle

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Then cosine can be found from ...

  cos(2x) = 1/√(tan(2x)² +1) = 1/√((-4/3)²+1) = √(9/25)

  cos(2x) = 3/5

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Sine can be found from these two:

  sin(2x) = cos(2x)tan(2x) = (3/5)(-4/3)

  sin(2x) = -4/5