Question

find value of
1. tan ( -25 pi/ 3 )
2. cosec ( -41 pi/ 4 )
3. cosec (-750 degree)
4. sec ( - 1470 degree)
5. cot ( 13 pi/ 4 )

Answer 1

Answer:

We are using a trigonometric relation, tanθ = sinθ/cosθ, to find the value of tan (pi/3).

We are using a reference triangle to calculate the values of sine and cosine. 

Since, θ = pi/3, therefore

sin(pi/3) = ⎷3/2, and

cos(pi/3) = 1/2

Now substitute sin(pi/3) = ⎷3/2, and cos(pi/3) = 1/2 in the equation tanθ = sinθ/cosθ 

tanθ = sinθ/cosθ

tan(pi/3) = sin(pi/3)/cos(pi/3)

tan(pi/3) = (⎷3/2)/(1/2)

 = ⎷3

Thus, the exact value of tan (pi/3) is ⎷3

I hooe you got it. Have a nice day.