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Title: Angle measurement (degrees, radians)

Grade: 1400-a Lesson: S3-L6

Explanation: Hello Students, time to practice and review the steps for the problem.

Lesson Steps

Step	Type	Explanation	Answer
1	Problem	Determine the measure of an angle in radians if its degree measure is 300.
2	Step	Write down the given angle in degrees:	angle = 300°
3	Hint	Use the conversion factor: There are \$pi/180\$ radians in one degree. So, to convert degrees to radians, multiply by \$pi/180\$
4	Step	Apply the conversion factor:	angle in radians = \$("angle in degrees") times \pi/(180°)\$
5	Step	Substitute the given angle into the formula:	angle in radians = \$300° times \pi/(180°)\$
6	Step	Cancel out 180 in the numerator and denominator	angle in radians = \$(300\pi)/180\$ angle in radians = \$(5\pi)/3\$
7	Step	So, the measure of the angle 300° in radians is \$(5\pi)/3\$radians.
8	Choice.A	This option doesn’t match the calculated value \$(5\pi)/3\$. It’s the reciprocal of the correct answer, so it is not a proper answer	\$3/(5 \pi)\$
9	Choice.B	This option suggests the angle measure is \$(3\pi)/5\$ radians, which is not equivalent to\$(5\pi)/3\$ radians	\$(3\pi)/5\$
10	Choice.C	This option matches the calculated value \$(5\pi)/3\$, representing the measure of the angle 300° in radians. It’s the correct answer	\$(5 \pi)/3\$
11	Choice.D	This option is not equivalent to the calculated value \$(5\pi)/3\$, It’s missing the 3 in the denominator, so it’s not correct	\$5/(pi)\$
12	Answer	Option	C
13	Sumup	Can you summarize what you’ve understood in the above steps?

Step

Type

Explanation

Answer

Problem

Determine the measure of an angle in radians if its degree measure is 300.

Step

Write down the given angle in degrees:

angle = 300°

Hint

Use the conversion factor:
There are \$pi/180\$ radians in one degree. So, to convert degrees to radians, multiply by \$pi/180\$

Step

Apply the conversion factor:

angle in radians = \$("angle in degrees") times \pi/(180°)\$

Step

Substitute the given angle into the formula:

angle in radians = \$300° times \pi/(180°)\$

Step

Cancel out 180 in the numerator and denominator

angle in radians = \$(300\pi)/180\$

angle in radians = \$(5\pi)/3\$

Step

So, the measure of the angle 300° in radians is \$(5\pi)/3\$radians.

Choice.A

This option doesn’t match the calculated value \$(5\pi)/3\$. It’s the reciprocal of the correct answer, so it is not a proper answer

\$3/(5 \pi)\$

Choice.B

This option suggests the angle measure is \$(3\pi)/5\$ radians, which is not equivalent to\$(5\pi)/3\$ radians

\$(3\pi)/5\$

Choice.C

This option matches the calculated value \$(5\pi)/3\$, representing the measure of the angle 300° in radians. It’s the correct answer

\$(5 \pi)/3\$

Choice.D

This option is not equivalent to the calculated value \$(5\pi)/3\$, It’s missing the 3 in the denominator, so it’s not correct

\$5/(pi)\$

Answer

Option

Sumup

Can you summarize what you’ve understood in the above steps?