Question

Express the following sexagesimal measure as radian measure and centennial system
i) 45° ii)270°

Answer 1

Answer:

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Step-by-step explanation:

1)

45°

In centisimal system

90° = 100 grade

dividing by 2 on both sides we get

45° = 50 grades

In Radian system

we know that

180° = π radians

Dividing by 4 we get

45° = (π/4) radians

2)

270°

In centisimal system

90° = 100 grade

Multiplying by 3 on both sides we get

270° = 300 grades

In Radian system

we know that

180° = π radians

Multiplying by 3/2 both sides we get

270° = (3π/2) radians

3)

72°

In centisimal system

90° = 100 grade

Dividing by 90 on both sides we get

1° = (100/90) grades

Multiplying by 72 on both sides we get

72° = 7200/90 = 720/9 grades = 80 grades

So

72° = 80 grades

In Radian system

we know that

180° = π radians

Dividing by 180 both sides we get

1° = (π/180) radians

Multiplying by 72 on both sides we get

72° = (72π/180) radians = (8π/20) radians = (2π/5) radians

So

72° = (2π/5) radians

4)

108°

In centisimal system

90° = 100 grade

Dividing by 90 on both sides we get

1° = (100/90) grades

Multiplying by 108 on both sides we get

108° = 10800/90 = 1080/9 grades = 120 grades

So

108° = 120 grades

In Radian system

we know that

180° = π radians

Dividing by 180 both sides we get

1° = (π/180) radians

Multiplying by 108 on both sides we get

108° = (108π/180) = (6π/10) = (3π/5) radians

So

108° = (3π/5) radians