Question

An acute angle θ is in a right triangle with cos θ = nine tenths. What is the value of sec θ?

Answer 1

Answer:$\frac{10}{9}$

Step-by-step explanation:

Trigonometric is made up of two words trigon and metric .

Trigon means triangle and metric means measurement .

Trigonometric ratios basically define the relationship between the angles and sides .

We talk about trigonometric ratios in a right angled triangle .

For any triangle , there are six trigonometric ratios .

We have trigonometric ratios : $\sin \theta \,,\,\cos \theta \,,\,\tan \theta \,,\,\csc \theta \,,\,\sec \theta \,,\,\cot \theta$ such that following relations hold :

$\csc \theta =\frac{1}{\sin \theta }\\\\\sec \theta =\frac{1}{\cos \theta }\\\\\cot \theta =\frac{1}{\tan \theta }$

Given: $\cos \theta =\frac{9}{10}$

To find : $\sec \theta$

Solution:

We know that $\sec \theta =\frac{1}{\cos \theta }$ , so , $\sec \theta =\frac{1}{\frac{9}{10} }=\frac{10}{9}$

Answer 2

We have
$\cos \theta=\frac{9}{10}$

For secant, we use
$\sec \theta=\frac{1}{\cos \theta}=\frac{1}{9/10}=\frac{10}{9}$