College Trigonometry, 2011a

758 Foundations of Trigonometry
We close this section with a few notes about solving equations which involve the circular functions.
First, the discussion on page 735 in Section 10.2.1 concerning solving equations applies to all six
circular functions, not just f(t) = cos(t) andg(t) =sin(t). In particular, to solve the equation
cot(t) =−1 for real numbers t, we can use the same thought process we used in Example 10.3.2,
number 3 to solve cot(θ) =−1 for angles θ in radian measure – we just need to remember to write
our answers using the variable t as opposed to θ. Next, it is critical that you know the domains
and ranges of the six circular functions so that you know which equations have no solutions. For
example, sec(t) = 1 2 has no solution because 1 2
is not in the range of secant. Finally, you will need to
review the notions of reference angles and coterminal angles so that you can see why csc(t) =−42
has an infinite set of solutions in Quadrant III and another infinite set of solutions in Quadrant IV.