Question

If tan0=-3/4 and 0 is in quadrant IV, cos20= (33/25, -17/25, 32/25, 7/25, 24/25?) and tan20= (24/7, -24/7, 7/25, -7/25, 13/7, -13/7?) PLEASE HELP. More information in the picture

Answer 1

Answer:

• cos(2θ) = 7/25
• tan(2θ) = -24/7

Step-by-step explanation:

Sometimes, it is easiest to let a calculator do the work. (See below)

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The magnitude of the tangent is less than 1, so the reference angle will be less than 45°. Then double the angle will be less than 90°, so will remain in the 4th quadrant, where the cosine is positive and the tangent is negative.

You can also use the identities ...

  cos(2θ) = (1 -tan(θ)²)/(1 +tan(θ)²)

  cos(2θ) = (1 -(-3/4)²)/(1 +(-3/4)²) = ((16-9)/16)/((16+9)/16)

  cos(2θ) = 7/25

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  tan(2θ) = 2tan(θ)/(1 -tan(θ)²) = 2(-3/4)/((16-9/16) = (-6/4)(16/7)

  tan(2θ) = -24/7