Question

Write the following angle measures in radians.

165°
A. π/3
B. π/2
C. π
D. 3π/4

-300°
A. -π/6
B. -π/2
C. -π
D. -5π/6

Answer 1

To convert angle measures from degrees to radians, multiply by π/180.

Step-by-step explanation:

In trigonometry and calculus, angles are often measured in radians, which is a unit of angular measure based on the radius of a circle. Radians are particularly useful in mathematical calculations involving circular motion, trigonometric functions, and calculus.

To convert angle measures from degrees to radians, we use the conversion factor π/180.

A. To convert 165 degrees to radians, we have

165 degrees * (π/180) = π/3 radians.

B. To convert 300 degrees to radians, we have

300 degrees * (π/180) = 5π/3 radians.

Therefore, the angle measures in radians are:

A. π/3 radians

B. 5π/3 radians

In trigonometric functions, angles in radians are often used. For example, the sine (

sin

⁡

sin), cosine (

cos

⁡

cos), and tangent (

tan

⁡

tan) functions typically take angles in radians as input.

It's important to be aware of whether an angle measure is given in degrees or radians, especially when working with mathematical expressions and functions that involve trigonometry or calculus.

Answer 2

To convert angle measures from degrees to radians, multiply the degree measure by (π radians/180°). 165° is equivalent to (11π/12) radians and -300° is equivalent to (-5π/3) radians.

Step-by-step explanation:

To convert angle measures from degrees to radians, we need to use the fact that 360 degrees is equal to 2π radians. So for the angle measure 165°, we can set up the following conversion:

165° * (π radians/180°) = (165π/180) radians = (11π/12) radians

Therefore, the angle measure 165° is equivalent to (11π/12) radians.

For the angle measure -300°, we can use the same conversion as above and also take into account that a negative angle is measured clockwise. So the conversion would be:

-300° * (π radians/180°) = (-300π/180) radians = (-5π/3) radians

Therefore, the angle measure -300° is equivalent to (-5π/3) radians.