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).