PLEASE ANSWER!!

Question

1. Convert 410 degrees to radians
2. convert 5pi over 4 to degrees

Answer 1

First, a way to remember these formulas rather than memorize them. For the unit circle, the circumference is 2π, and the circle has 360°. Thus, we go from radians to degrees by multiplying by 360°/2π = 180°/π, and we go from degrees to radians by multiplying by π/180°

Thus, 410° = 410° * π/180° = 41/18 π or 2 5/18 π

5π/4 = 5π/4 * 180°/π = 900°/4 = 225°

Note: when radians are expressed in units of π fractions, where the fraction has 2, 3, 4, or 6 in the denominator, especially when the fraction is between 0 and 2, you should get to know it

Answer 2

For angle conversion problems like this, we use the fact that 180 degrees is equal to pi radians, and the conversion itself involves the unit fractions ( i.e. a fraction whose value is 1) 180/pi or its reciprocal pi/180.

For the first problem of converting to radians, we take the original measure of 410 degrees and multiply it by whichever unit fraction above will allow us to cancel out the original unit of measure ( i.e. degrees) and keep the desired unit of measure ( i.e. radians) for our final answer. So we set up the multiplication problem like this: 410 degrees x (pi radians/180 degrees). The "degrees" will cancel, the radians will be left as the only unit of measure, and we simply divide 410 pi by 180 to get our result. So it looks like this: 410(pi) / 180, and if we simply reduce the fraction and leave pi as pi, it results in 41 pi/18 radians.

For the second problem, converting radians to degrees, we will "flip" our unit fraction over so now the pi radians will cancel and the only unit of measure left will be degrees. The expression will look like this:

(5 pi/4 radians) x (180 degrees/pi radians). The "pi" and the "radians" will now cancel out, leaving us with just the degree unit of measure, and we need only multiply 5/4 by 180 to get our result of 225 degrees.