Question

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

Answer 1

We have

`\cos \theta=(9)/(10)`

For secant, we use

`\sec \theta=(1)/(\cos \theta)=(1)/(9/10)=(10)/(9)`

Answer 2

Answer:
`(10)/(9)`

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 =(1)/(\sin \theta )\\\\\sec \theta =(1)/(\cos \theta )\\\\\cot \theta =(1)/(\tan \theta )`

Given:
`\cos \theta =(9)/(10)`

To find :
`\sec \theta`

Solution:

We know that
`\sec \theta =(1)/(\cos \theta )` , so ,
`\sec \theta =(1)/((9)/(10) )=(10)/(9)`