
Kenneth S. answered 05/27/16
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Expert Help in Algebra/Trig/(Pre)calculus to Guarantee Success in 2018
If this is your classwork, then you must have been introduced to appropriate 'double angle' formulas.
It should be easy to obtain sin θ = 4/5, either by recognizing the 3-4-5 triangle situation, or by using the fundamental Pythagorean identity.
sin 2θ = 2 sin θ cos θ = 2(4/5)(3/5) = 24/25. Now use one of the 3 versions of the formula for cos 2θ.