## anonymous 3 years ago use the unit circle to find the value of the trigonmetric function. csc pi/3

1. UnkleRhaukus

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2. UnkleRhaukus

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3. UnkleRhaukus

because we are using a Unit circle, ie a circle with radius one, the hypotenuse of the triangle is 1

4. UnkleRhaukus

the angle theta is π/3

5. anonymous

sorry i still dont get it

6. anonymous

is the answer 1/ sin(pi/3)=squareroot of 3

7. UnkleRhaukus

ops **$\csc(\theta)=\frac1{\sin(\theta)}=\frac{1}{\text{opposite/hypotenuse}}=\frac{\text{hypotenuse}}{\text{opposite}}$

8. anonymous

thats what i did from my book :(

9. UnkleRhaukus

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10. anonymous

since $\Large \csc(\theta) =\frac {hyp}{opp}=\frac{1}{\sin(\theta)}$ for $\frac{\pi}{3}$ since it is unit circle hyp =1 x=1/2 and $y=opp=\frac{\sqrt{3}}{2}$ so $\[\Large \csc({\frac{\pi}{3}})=\frac{1}{\frac{\sqrt{3}}{2}}$ $\Large \csc \frac{\pi}{3}=\frac{2}{\sqrt{3}}$

11. anonymous

i get it now thank u so much : )

12. anonymous

you welcome :)

13. anonymous

can u tell if this one is right cos pi/3 =square root of 3

14. anonymous