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...
Look at the position of theta from
tan (theta) = 4/3, pi < theta < (3pi)/2
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
pi < theta < (3pi)/2 , now divide by 2
pi/2 < theta/2 < (3pi)/4
which is in the second quadrant, and the cosine of a second quadrant angle is also negative.