Answers and Explanations

TRIGONOMETRY FOLLOW-UP TEST

1 . E

Since   you are given   the opposite    and adjacent    sides,  try using   tangent.

Now use the tan–1   function    on  your    calculator  (probably   “2nd”   and then    “tan”)  to  find

tan–1(1.25) =   51.34019175

This    is  closest to  (E).

2 . E

Whenever    you have    a   complicated expression  with    trigonometric   functions,  try factoring.

First   factor  out sin θ   from    each    term:

sin^3 θ +   sin θ   –   sin θ   cos^2 θ =   (sin    θ)(sin^2 θ  +   1   –   cos^2 θ)

Next    look    for identities  or  ways    to  use the definitions of  the trig    functions.  In  this    case,   you

should  notice  that    1   –   cos^2 θ =   (sin^2 θ),  so

3 . A

You could   use the given   equation     to find    θ,  but that’s  not really  necessary.

You could   re-express  the given   equation    putting it  all in  terms   of  sin θ: