Answer:
sin(2x) = 120/169
Explanation:
A suitable calculator can figure this for you. (See below)
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You can make use of some trig identities:
- sin(2x) = 2sin(x)cos(x)
- sec(x)² = tan(x)² +1
- cos(x) = 1/sec(x)
- tan(x) = sin(x)/cos(x)
Then your function value can be written as ...
sin(2x) = 2sin(x)cos(x) = 2(sin(x)/cos(x))cos(x)² = 2tan(x)/sec(x)²
= 2tan(x)/(tan(x)² +1)
Filling in the given value for tan(x), this is ...
sin(2x) = 2(12/5)/((12/5)² +1) = (24/5)/(144/25 +1) = (120/25)/((144+25)/25)
sin(2x) = 120/169