Question

tan13pi/4 A. Use the fact that there are 2pi radians in each circle to find another angle, smaller than 2 pi, that is equivalent to 13pi/4. B. Find the tangent of the angle you found in part A. This is also 13pi/4.

Answer 1

hello :
13π/4 = (16-3)π/4
= 16π/4 -3π/4
13π/4 = -3π/4 +4π
tan( 13π/4) = tan ( -3π/4)= - tan ( 3π/4) =- tan( π - π/4) = - tan(- π/4)
tan( 13π/4) = -(-tan(π/4)) =tan(π/4)=1

Answer 2

1

Explanation:

Tan 13π/4 = tan(3π + 1/4π)

According to the trigonometry identity;

tan(A+B) = tanA + tanB/1-tanAtanB

If A = 3π and B = π/4

tan(3π + 1/4π) = tan 3π + tanπ/4/1-tan3πtanπ/4

If πrad = 180°

tan(3π + 1/4π) = tan 540° + tan45°/1-tan540°tan45°

tan(3π + 1/4π) = 0+1/1-0(1)

tan(3π + 1/4π) = 1/1-0

tan(3π + 1/4π) = 1/1

tan(3π + 1/4π) = 1

tan 13π/4 = 1