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Find sin(2x), cos(2x), and tan(2x) from the given information.

User Jasiry
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Final answer:

To calculate sin(2x), cos(2x), and tan(2x), one uses the double-angle trigonometric identities along with the known values of sin(x) and cos(x) provided from the right triangle or other given information.

Step-by-step explanation:

To find sin(2x), cos(2x), and tan(2x) based on the given information, we can employ trigonometric identities. We know that:

  • sin(2x) = 2sin(x)cos(x)
  • cos(2x) = cos²(x) - sin²(x) or 2cos²(x) - 1 or 1 - 2sin²(x)
  • tan(2x) can be found using the identity tan(2x) = sin(2x)/cos(2x) or by the identity tan(2x) = 2tan(x)/(1 - tan²(x)) if tan(x) is known.

If the original questions provide specific values for sin(x) and cos(x), or the value of x itself, these can be directly substituted into the above formulas to calculate sin(2x), cos(2x), and tan(2x).

User Nighteen
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