SAT Math Problem (10)

Question

If 0 < x < 2π and 5 cos[x] = sqrt[5], what is the value of (sin[x]/3)³?

Answer 1

it appears that cos x = 1/√5.

 

So sin x = sqrt (1-cos²x) = sqrt (1-1/5) = sqrt(4/5) = ±2/√5; there are two answers because the positive cosines are in quadrant II or III, so associated sines are positive or negative, respectively.

 

Now you can compute (sin[x]/3)³ using this information, i.e. finish the job by taking one third of ±2/√5, and then cube it!

You may want to rationalize denominator, but that's really not necessary.

 

HINT: use the calculator to check your answers.