Question

If cos(t)=−9/11 where π<t<3π2, 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

Answer:

$cos(\frac{t}{2} ) = -\sqrt\frac{1}{11}$

Step-by-step explanation:

The relationship between cos(t) and cos($\frac{t}{2}$) is:

$cos(\frac{t}{2} ) = a\sqrt\frac{1+cos(t)}{2}$

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

Thus, $cos(\frac{t}{2} ) = -\sqrt\frac{1-\frac{9}{11}}{2}$

⇒  $cos(\frac{t}{2} ) = -\sqrt\frac{11-9}{2\times 11}$

⇒ $cos(\frac{t}{2} ) = -\sqrt\frac{2}{22}$

⇒ $cos(\frac{t}{2} ) = -\sqrt\frac{1}{11}$