Question

Algebra 2 Help!

What are the sine, cosine, and tangent of 5pi/3 radians?

sin Θ = -sqrt 3/2; cos Θ = 1/2; tan Θ = -sqrt 3

sin Θ = sqrt 3/2; cos Θ = -1/2; tan Θ = sqrt 3

sin Θ = sqrt 3/2; cos Θ = 1/2; tan Θ = sqrt 3

sin Θ = -sqrt 3/2; cos Θ = -1/2; tan Θ = -sqrt 3

Answer 1

`sin((5\pi )/(3))=-(√(3))/(2)` ;
`cos((5\pi )/(3))=(1)/(2)` ;
`tan((5\pi )/(3))=-√(3)`

Explanation:

we know that

`\pi \ radians=180\ degrees`

so

`(5\pi )/(3)\ radians=300\ degrees`

The angle belong to the IV quadrant

therefore

The sine is negative

The cosine is positive

The tangent is negative

`360\°-300\°=60\°`

so

`sin((5\pi )/(3))=-sin(60\°)=-(√(3))/(2)`

`cos((5\pi )/(3))=cos(60\°)=(1)/(2)`

`tan((5\pi )/(3))=-tan(60\°)=-√(3)`

Answer 2

Base on the question that ask to calculate the sine, cosine, and tangent of 5pi/3 radians and base on my further calculation, I would say that the answer would be sin Θ = -sqrt 3/2; cos Θ = -1/2; tan Θ = -sqrt 3. I hope you are satisfied with my answer and feel free to ask for more if you have question and further clarification