Question

Given sin(theta)= 7/11 and sec(theta)<0
Find cos(theta) and tan(theta)

Answer 1

cos∅ =
`-(6√(2) )/(11)`

Explanation:

Answer 2

When given a trigonometric ratio, and asked to find another ratio, we draw a right triangle as shown in the picture.

From the pythagorean theorem we find the length of AB:


`|AB|= \sqrt{ AC^(2)- BC^(2) }= \sqrt{ 11^(2)- 7^(2) }= √(121-49) = √(72) = √(2*36)`
`= 6√(2)`

the numerical value of

cos∅=adjacent side/hypotenuse=
`( 6 √(2) )/(11)`

since sec∅=1/cos∅, and sec∅ is negative, then cos∅ is also negative.


Answer:

cos∅=
`-( 6 √(2) )/(11)`