Question

1. For which angle is secant undefined?

a. 30°
b. 45°
c. 180°
d. 270°

2. Which of the following is csc(-166°) equal to?

a. csc⁡(14°)
b. -csc⁡(14°)
c. -csc⁡(-14°)
d. csc⁡(166°)

Answer 1

1. 180 aparently
2. stil looking
im in the same delima

Answer 2

1. The secant is defined as the inverse function of co-secant or cos function

Hence when the cosine is 0, the secant is 1/0 which is undefined. So, when cosine is 0, secant is undefined

Cos 30 =
`√(3) /2`

Cos 45 =
`1/√(2)`

Cos 180 = -1

cos 270 =0

Since cos 270 is 0, secant of 270 is undefined

Answer is d: 270

2. cosec (-x) = - cosec (180 -x)

We have cosec(-166) = - cosec (180-14) = -cosec (14)

Alternatively we can confirm this as csc (-166) = -4.133565 and -csc(14) = -4.133565; Hence, we can reconfirm that the answer arrived at is right

Therefore csc (-166) = -csc(14) (Option B) is the right answer