Question

If csc B = b, which number below is not a possible value of b?

-1.75
0.5
1
1.05

Answer 1

Answer:

0.5

Step-by-step explanation:

$\csc B=\dfrac{1}{\sin B}\\\\-1\leq\sin B\leq1,\ \text{therefore}\ \csc B\leq-1\ or\ \csc B\geq1\\\\-1.75\leq-1\\\\0.5\to \bold{ANSWER}\\\\1\geq1\\\\1.05\geq1$

Answer 2

By definition, the cosecant is the inverse of the sine:

$\csc(x) = \dfrac{1}{\sin(x)}$

Since the sine is never more than 1, the cosecant can never be smaller than 1.

So, the only impossible option is 0.5.