Find the six trigonometric functions of t. a) t = 5*pi over 3 b) t = -7*pi over 6

Expert Answers

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a) `sin(5Pi/3)=sin(2Pi-Pi/3)=-sin(Pi/3)=-sqrt(3)/2`

`cos(5Pi/3)=cos(Pi/3)=1/2`

`tan(5Pi/3)=-tan(Pi/3)=-sqrt(3)`

`cot(5Pi/3)=-cot(Pi/3)=-1/(sqrt(3))=-sqrt(3)/3`

`csc(5Pi/3)=-2/sqrt(3)=-[2sqrt(3)]/3`

`sec(5Pi/3)=2`

b) `sin(-7Pi/6)=sin(5Pi/6)=1/2`

`cos(-7Pi/6)=-sqrt(3)/2`

`tan(-7Pi/6)=-1/sqrt(3)=-sqrt(3)/3`

`cot(-7Pi/6)=-sqrt(3)`

`sec(-7Pi/6)=-2/sqrt(3)=-[2sqrt(3)]/3`

`csc(-7Pi/6)=2`

 

 

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