SOLUTION: a. Let f (x) =&#8730;(49 - x^2)/x and g(t) = 7 sin t for 0 &#8804; t < &#960;/2. Find f(g(t)) and simplify to a single trig function (no trig functions in a denominator).

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Question 920587: a. Let
f (x) =√(49 - x^2)/x

and g(t) = 7 sin t for 0 ≤ t < π/2. Find f(g(t)) and simplify to a single trig function (no trig
functions in a denominator).
b. Simplify and evaluate: cos(2π/15)cos(7π/15)+ sin(2π/15)sin(7π/15)

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
a. Let
f (x) =√(49 - x^2)/x and g(t) = 7 sin t for 0 ≤ t < π/2.
Find f(g(t)) and simplify to a single trig function (no trig functions in a denominator).
f(g(t)) = f(7*sin(t)) = sqrt[49-49sin^2(t)] = 7sqrt(1-sin^2(t)) = 7cos(t)
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b. Simplify and evaluate: cos(2π/15)cos(7π/15)+ sin(2π/15)sin(7π/15)
= cos[(2pi/15)-(7pi/15)] = cos[-pi/3] = cos(pi/3) = 1/2
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Cheers,
Stan H.
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SOLUTION: a. Let f (x) =&#8730;(49 - x^2)/x and g(t) = 7 sin t for 0 &#8804; t < &#960;/2. Find f(g(t)) and simplify to a single trig function (no trig functions in a denominator).

SOLUTION: a. Let f (x) =√(49 - x^2)/x and g(t) = 7 sin t for 0 ≤ t < π/2. Find f(g(t)) and simplify to a single trig function (no trig functions in a denominator).