Question

I hope that the back of the book is wrong the back of the book tells me that the answer is - SQRT(5)/5

I get positive square root( 5) divided by 5

can you tell me if the answer is positive or negative if it is negative can you please explain why? Thanks!

tan (theta) = 4/3, pi < theta < (3pi)/2

what is cos (theta/2)

I get positive SQRT(5)/5
the back of the book tells me negative and I do not see why or how...

Answer 1

Look at the position of theta from

tan (theta) = 4/3, <b>pi < theta < (3pi)/2</b>

so isn't theta in the third quadrant?
and isn't the cosine of an angle in the third quadrant negative?

then since you have
<b>pi < theta < (3pi)/2</b> , now divide by 2
<b>pi/2 < theta/2 < (3pi)/4</b>
which is in the second quadrant, and the cosine of a second quadrant angle is also negative.