Which of the following best explains why tan5π/6 ≠ tan5π/3

The angles do not have the same reference angle.

Step-by-step explanation:

1) Angle 5π / 3 radians:

Convert radians to degrees: 5π/3 × 180° / π = 300°

300° is in the fourth quadrant

The reference angle for angles in the fourth quadrant is 360° - angle ⇒ 360° - 300° = 60°.

∴ The reference angle for this angle is 60°.

2) Angle 5π / 6 radians:

Convert radians to degrees: 5π/6 × 180° / π = 150°

150° is in the second quadrant

The reference angle for angles in the second quadrant is 180° - angle ⇒ 180° - 150° = 30°.

∴ The reference angle for this angle is 30°.

3) Conclusion:

Since the reference angles are different, the tangent ratios have different values.

tan (5π/3) = - tan(60°) = - √3

tan (5π/6) = - tan(30°) = - (√3)/3

Note that the tangent is negative in both second and fourth quadrants.

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hello from mrbilldoesmath!

answer:   x^2 + y^2 = 1024

discussion:

the equation of a circle with center (h,k) and radius "r" is

(x-h)^2 + (y-k)^2 = r^2.

in our case

(x-0)^2 + (y-0) ^2 = 32^2 = 1024

you,

mrb