College Algebra & Trigonometry, 2018a

466 CHAPTER 10. TRIGONOMETRIC IDENTITIES AND EQUATIONS
10.4 More Trigonometric Equations
When the solution to a trigonometric equation is one of the quadrantal angles
(0 ◦ ,90 ◦ , 180 ◦ , 270 ◦ and so on), then determining all the solutions between 0 ◦ and
360 ◦ can work a little differently. The calculator will return some of these values,
but in some cases it may not. If we go back to the unit circle, we can see this more
clearly:
(cos 90 ◦ , sin 90 ◦ )
(0, 1)
(cos 180 ◦ , sin 180 ◦ )
(−1, 0)
(cos 0 ◦ , sin 0 ◦ )
(1, 0)
(0, −1)
(cos 270 ◦ , sin 270 ◦ )
In the diagram above we can see the sine and cosine for 0 ◦ ,90 ◦ , 180 ◦ , and 270 ◦ .
Since tan θ = sin θ
cos θ , then we can see that tan 0◦ =0, tan 90 ◦ is undefined, tan 180 ◦ =
0 and tan 270 ◦ is also undefined.
The real issue with the quadrantal angles is finding sin −1 (0), cos −1 (0) or tan −1 (0).
The calculator returns values of:
sin −1 (0) = 0 ◦
cos −1 (0) = 90 ◦
tan −1 (0) = 0 ◦
In each case, there is another possibility than differs from the given angle by 180 ◦ ,
so: