Question

What are the values that satisfy the trigonometric equation for: 0 < q < 2?

Sinθ + tan(-θ) = 0

Answer 1

\(\bf sin(\theta)+tan(-\theta)=0\\ \quad \\ \quad \\

sin(\theta)+\cfrac{sin(-\theta)}{cos(-\theta)}=0\\
\textit{recall that}\qquad \color{blue}{sin(-x) = -sin(x)\qquad and\qquad cos(-x) = cos(x)}\\ \quad \\
sin(\theta)+\cfrac{sin(-\theta)}{cos(-\theta)}=0\implies sin(\theta)+\cfrac{-sin(\theta)}{cos(\theta)}=0\\
\textit{let's take common factor to the left side}\\ \quad \\
sin(\theta)\left[1+\frac{-1}{cos(\theta)}\right]=0\implies sin(\theta)\left[1-\frac{1}{cos(\theta)}\right]=0\)


and I think you can get the angles from there

Answer 2

no not to sure

Answer 3

ok.... let's break those down further then

\(\bf sin(\theta)\left[1-\frac{1}{cos(\theta)}\right]=0\\ \quad \\
\implies
\begin{cases}
sin(\theta) =0\\ \quad \\
\bf 1-\frac{1}{cos(\theta)}=0\implies 1=\frac{1}{cos(\theta)}\implies cos(\theta) = 1
\end{cases}\)

Answer 4

can you the angle(s) now?

Answer 5

its 1

Answer 6

well... cosine is 1, and sine is 0
yes
those are the values of the functions
the angles are AT where sine is 0, and also where cosine is 1

check your Unit Circle to find out where, is sine = 0 and cosine = 1

Answer 7

what is a unit circle

Answer 8

well, if you don't have one, do get one, many you can find online -> http://i1.cpcache.com/product_zoom/627420071/large_unit_circle_clock.jpg

Answer 9

the pair of numbers there, are the (x, y) values, or the (cosine, sine) pair as well