Evaluate (if possible) the sine,cosine, and tangent of the angle

10pi/3

10π/3 - 2π = 3π/2

then see

http://www.jiskha.com/display.cgi?id=1307390418

(10pi/3)rad * (1/2pi)rev/rad = 5/3 =

1 2/3 rev.
2/3 rev * 360deg/rev = 240 deg.

sin(240) = -0.8660 = -(sqrt3)/2.

cos(240) = -0.50 = -1/2.

tan(240) = 1.732 = sqrt3.

240 deg. = 4pi/3 rad.

To evaluate the sine, cosine, and tangent of an angle, we need to know the angle in radians. In this case, the given angle is 10π/3.

Let's start with the sine of the angle. The sine function (sin) represents the ratio of the length of the side opposite the angle to the length of the hypotenuse in a right triangle.

To calculate the sine of 10π/3, we can use the unit circle. In the unit circle, the angle 10π/3 is equivalent to 2π/3 (since rotating a full circle of 2π does not change the sine value).

The unit circle shows that at 2π/3, the sine value is equal to √3/2. Therefore, the sine value of 10π/3 is also √3/2.

Moving on to the cosine function (cos), it represents the ratio of the length of the adjacent side to the length of the hypotenuse in a right triangle.

Using the unit circle, at 2π/3, the cosine value is -1/2. Therefore, the cosine value of 10π/3 is also -1/2.

Lastly, the tangent function (tan) represents the ratio of the sine of the angle to the cosine of the angle.

To find the tangent of 10π/3, we can divide the sine value (√3/2) by the cosine value (-1/2). This gives us (-√3/2) / (-1/2), which simplifies to √3.

Therefore, the sine (sin) of 10π/3 is √3/2, the cosine (cos) of 10π/3 is -1/2, and the tangent (tan) of 10π/3 is √3.