SAT Subject Test Mathematics Level 2

Here’s a question that looks like a complicated trigonometry question but turns out not to be
trigonometry at all.

PICK A POINT OR TWO

To  identify    the equation    for a   particular  graph,  pick    a   point   or  two from    the graph   and try the

coordinates in  the equations.

Example 5

DON’T BE FOOLED BY DISGUISES

Sometimes   what    looks   like    a   trigonometry    question    turns   out to  be  primarily   an  algebra

question.

This sure looks like a trigonometry question. There are sines and thetas all over the place. But in fact
this is just a plain old algebra question in disguise. You never need to find the sine or the arcsine of
anything. You don’t need to find θ. This is really just a quadratic equation where the unknown is
written “sin θ” instead of the more usual “x.” Perhaps you’ll find the equation easier to deal with if
you first replace “sin θ” with x :

1. If   6sin^2 θ    –   sin θ   =   1   and 0   ≤   θ   ≤   π,  what    is  the value   of  sin θ?

(A)

(B)

(C)

(D) 19

(E) 30