Question

Please answer these questions

Answer 1

Explanation:

(1)The units for measuring angles are degrees and radians

A circle is 360° which is equal to 2π radians

1°=π/180

To convert angle measurement from degrees to radians multiply the value of degrees by π/180

(11)

To convert angle measurement from radians to degree multiply the value of radian by 180/π

(111)Yes it matters because you will use different formulas to calculate the length of the arc

For example , when the central angle is in radians, the formula to apply is;

⇒ S=rФ -------------where r is the radius of circle and Ф is angle in radians and S is the arc length.

⇒ When the central angle value is in degrees , the formula to apply is

Arc length =2πr×(Ф/360) where Ф is in degrees , r is radius of circle

2.
`sin(17\pi )/(6) \\`

we know π=180°

hence 17/6 π=?---------------cross multiply

`(17\pi )/(6) *180\\\\\\=17\pi *30\\\\\\=510\pi`

Apply trigonometry

Find sine 510°

Sine (510°-360°)= sine 150°

Sine 150° = sine 30° = 1/2-----------------2nd quadrant

This means sine 510° = 1/2