Question

Find the exact value of sec(–135°).

Answer 1

-
`√(2)`

Explanation:

Answer 2

Answer:
`-√(2)`

Explanation:

The trigonometric function secant is the reciprocal of cosine:

`sec(\alpha)=(1)/(cos(\alpha))`

For
`-135\°`:

`sec(-135\°)=(1)/(cos(-135\°))` (1)

On the other hand, it is known
`cos(-\alpha)=cos(\alpha)`, hence:

`cos(-135\°)=cos(135\°)` (2)

In addition, it is known
`cos(135\°)=-cos(45\°)=-(√(2))/(2)` (3)

Substituting this on (1):

`sec(-135\°)=(1)/(-(√(2))/(2))` (4)

`sec(-135\°)=-(2)/(√(2))` (5)

`sec(-135\°)=-(2)/(√(2))((√(2))/(√(2)))` (6)

Finally:

`sec(-135\°)=-√(2)`