Question

If  cos(t)=− 9/11

 where  π<t< 3π 2 , find the values of the following trigonometric function  cos(t/2)

Answer 1

cos(t/2) I got .45 is that what you were looking for or do I need to plug it into the equation up top? can you give me notes of something? cos( -9/11/2) = .45

Answer 2

`cos((t)/(2) ) = -\sqrt(1)/(11)`

Explanation:

The relationship between cos(t) and cos(
`(t)/(2)`) is:

`cos((t)/(2) ) = a\sqrt(1+cos(t))/(2)`

where a is equal to +1 or -1 is same as same sign which cos(t) holds.

Thus,
`cos((t)/(2) ) = -\sqrt(1-(9)/(11))/(2)`

⇒
`cos((t)/(2) ) = -\sqrt(11-9)/(2* 11)`

⇒
`cos((t)/(2) ) = -\sqrt(2)/(22)`

⇒
`cos((t)/(2) ) = -\sqrt(1)/(11)`