Question

which of the following trigonometric equations is false for x?
a) sin x = 2 /√5
b) cos x = -0.1439
c) cos² x + sin² x = 1
d) sec x = √3 / 4
e) tan x = -100

Answer 1

ANSWER

$\sec(x) = \frac{ \sqrt{3} }{4}$


EXPLANATION


The correct answer is option D.

The value of the basic cosine function is between negative one and one.

That is for
$f(x)= \cos(x)$
the range of f is
$[-1,1]$

The given equation in option D is

$\sec(x) = \frac{ \sqrt{3} }{4}$

We know that the secant function is the reciprocal of the cosine function.

This implies that,

$\cos(x) = \frac{4}{ \sqrt{3} } = \frac{4 \sqrt{3} }{3}$


This value is more than 1. It is not within the range of the cosine function, hence it is false because it is not defined.