Find the exact value of sec(–135°).

Question

asked Sep 22, 2020 8.1k views

2 Answers

JChan · Answer 1 · 2020-09-27T17:21:30+0000

Answer:

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:

$sec(-135\°)=-√(2)$