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In this lesson, we will learn how to covert degrees to radians.

Q1:

Convert the following angle sizes from degrees to radians. Give your answers in terms of in their simplest form.

Q2:

Convert the following angle sizes from radians to degrees. Give your answers to the nearest degree where necessary.

radians

Q3:

What is the equivalent size of in radians?

Q4:

Convert 3 6 0 ∘ to radians giving the answer in terms of 𝜋 .

Q5:

Two angles in a triangle are 5 5 ∘ and 7 𝜋 1 8 r a d i a n s . Find the value of the third angle giving the answer in radians in terms of 𝜋 .

Q6:

The shadow of a sundial changes at a rate of 1 5 ∘ every hour. After how many hours will the shadow have rotated by an angle of 𝜋 radians?

Q7:

Convert − 1 0 5 ∘ into radians in terms of 𝜋 .

Q8:

Find the values of two supplementary angles in radians given the difference between the angles is 𝜋 4 5 .

Q9:

Two angles in a triangle are 𝜋 6 and 8 𝜋 1 5 . Find the value of the third angle giving the answer in radians in terms of 𝜋 .

Q10:

Find the size of the smaller angle between the hour and minute hands at half past nine giving the answer in radians.

Q11:

What is the perimeter of a unit circle in terms of 𝜋 ?

What is the angle of a complete rotation?

What is the length of the arc in a unit circle subtended by an angle of 𝜋 4 ?

Which fraction of a complete rotation does an angle of 𝜋 4 correspond to?

Q12:

Convert 6 0 ∘ to radians giving the answer in terms of 𝜋 .

Q13:

Convert − 7 0 ∘ into radians in terms of 𝜋 .

Q14:

Two angles in a triangle are 2 0 ∘ and 1 1 𝜋 3 6 r a d i a n s . Find the value of the third angle giving the answer in radians in terms of 𝜋 .

Q15:

The shadow of a sundial changes at a rate of 1 5 ∘ every hour. After how many hours will the shadow have rotated by an angle of 𝜋 4 radians?

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