Question

URGENT!!! Given that cosine theta = x/6. Which expression represents theta in terms of x?

A. Arccos(x/6)
B. Cos(x/6)
C. Sin(x/6)
D. Arcsin(x/6)

Answer 1

Answer: arccos(x/6) which is choice A

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Step-by-step explanation:

If we had something like 6*x = 12, then we would divide both sides by 6 to isolate x. Note how division is the inverse operation of multiplication. "inverse" is just a fancy word that means "opposite" more or less. So division is the opposite of multiplication. It undoes whatever multiplication is doing.

In a similar fashion, the arc trig functions undo the regular trig functions. In this case we have a cosine applied to theta. To undo the cosine operation, we use the arccosine function which is arccos for short. So we have this

cos(theta) = x/6)

arccos( cos(theta) ) = arccos(x/6) ... apply arccos to both sides

theta = arccos(x/6) ... note how the "arccos" and "cos" cancel out on the left side

note: your calculator may have the notation
`cos^(-1)` (cos with a -1 as an exponent) which is basically the same thing as arccosine.