SOLUTION: Determine the exact values of each expression for the given value of θ. Note: Your answers must be in EXACT form. They cannot contain decimals. If an answer involves a squa

Algebra ->  Trigonometry-basics -> SOLUTION: Determine the exact values of each expression for the given value of θ. Note: Your answers must be in EXACT form. They cannot contain decimals. If an answer involves a squa      Log On


   

Question 966018: Determine the exact values of each expression for the given value of θ.
Note: Your answers must be in EXACT form. They cannot contain decimals. If an answer involves a square root, write it as sqrt . For instance, the square root of 2 should be written as sqrt(2).
If θ=π/3, then tan(2θ)=
If θ=π/8, then cot(2θ)=
If θ=π/2, then sec(θ/2)=
If θ=5π/2, then csc(θ/2)=

Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Determine the exact values of each expression for the given value of θ.
Note: Your answers must be in EXACT form. They cannot contain decimals. If an answer involves a square root, write it as sqrt . For instance, the square root of 2 should be written as sqrt(2).
If θ=π/3, then tan(2θ)=
If θ=π/8, then cot(2θ)=
If θ=π/2, then sec(θ/2)=
If θ=5π/2, then csc(θ/2)=
**
use x for theta
x=pi/3
tan(2x)=tan(2pi/3)=-sqrt%283%29
..
x=pi/8
cot(2x)=cot(pi/4)=1
..
x=pi/2
cos(x/2)=sin((pi/2)/2)=sqrt%28%281%2Bcos%28pi%2F2%29%29%2F2%29=sqrt%281%2F2%29=1/√2
sec(x/2)=1/cos(x/2)=√2
..
x=5pi/2
sin(x/2)=sin((5pi/2)/2)=sqrt%28%281-cos%285pi%2F2%29%29%2F2%29=sqrt%281%2F2%29=1/√2
csc(x/2)=1/sin(x/2)=√2
note:
cos(pi/2)=0
cos(5pi/2)=0