Question

If sin theta< 0 and tan theta< 0 then:

A. 0 < theta < 90
B. 90 < theta < 180
C. 180 < theta < 270
D. 270 < theta < 360

Answer 1

\(\bf sin theta< 0 and tan theta< 0 then:\\
sin(\theta)<0\qquad \textit{another way of saying }sin(\theta)\textit{ is negative}\\ \quad \\
tan(\theta) <0 \textit{another way of saying }tan(\theta)\textit{ is negative}\\ \quad \\
tan(\theta)=\cfrac{sin(\theta)}{cos(\theta)}\implies \cfrac{{\color{red}{ negative}}}{{\color{blue}{ positive}}}\implies {\color{blue}{ cos(\theta) > 0}}\textit{ or is positive}\)

now... check your Unit Circle to see where the cosine and sine are such values

Answer 2

woops I pasted too much but anyhow \(\bf
sin(\theta)<0\qquad \textit{another way of saying }sin(\theta)\textit{ is negative}\\ \quad \\
tan(\theta) <0 \textit{another way of saying }tan(\theta)\textit{ is negative}\\ \quad \\
tan(\theta)=\cfrac{sin(\theta)}{cos(\theta)}\implies \cfrac{{\color{red}{ negative}}}{{\color{blue}{ positive}}}\implies {\color{blue}{ cos(\theta) > 0}}\textit{ or is positive}\)

check your Unit Circle

Answer 3

Hint both sine and tangent are negative in the fourth quadrant