Final answer:
The sine (sin) function gives the ratio of the length of the side opposite to an angle in a right triangle to the hypotenuse, while the tangent (tan) function gives the ratio of the length of the side opposite to an angle to the side adjacent to the angle.
Step-by-step explanation:
The sine (sin) and tangent (tan) functions are mathematical functions commonly used in trigonometry. The sine function gives the ratio of the length of the side opposite to an angle in a right triangle to the hypotenuse, while the tangent function gives the ratio of the length of the side opposite to an angle to the side adjacent to the angle.
To calculate sin(pi/6), you can use the fact that pi/6 is equivalent to 30 degrees. In a right triangle with a 30 degree angle, the side opposite the angle is 1/2 of the hypotenuse, so sin(pi/6) is equal to 1/2.
To calculate tan(pi/4), you can use the fact that pi/4 is equivalent to 45 degrees. In a right triangle with a 45 degree angle, the side opposite the angle is equal to the side adjacent to the angle, so tan(pi/4) is equal to 1.
To calculate sin(pi/6), you can use the fact that pi/6 is equivalent to 30 degrees. In a right triangle with a 30 degree angle, the side opposite the angle is 1/2 of the hypotenuse, so sin(pi/6) is equal to 1/2.
To calculate tan(pi/4), you can use the fact that pi/4 is equivalent to 45 degrees. In a right triangle with a 45 degree angle, the side opposite the angle is equal to the side adjacent to the angle, so tan(pi/4) is equal to 1.