Exercise 90 Page 461

When we know the number of radians in π form, we can convert to degrees by letting 180^(∘) equal π.

Converting from degrees to radians

If we divide both sides of our equation by 180^(∘), we get a new equation that describes the number of radians that 1^(∘) represents. 180^(∘)=π rad ⇔ 1^(∘) = π/180^(∘) rad Now we can multiply both sides of this equation by an arbitrary number of degrees to determine how many radians that number of degrees is equal to. Let's determine the number of radians that 90^(∘) equals.

1^(∘) =π/180^(∘) rad

MultEqn

LHS * 90=RHS* 90

90^(∘) =π/180^(∘)* 90^(∘) rad

MoveRightFacToNum

a/c* b = a* b/c

90^(∘) =π* 90^(∘)/180^(∘) rad

ReduceFrac

a/b=.a /90^(∘)./.b /90^(∘).

90^(∘) =π/2 rad

If we multiply a given number of degrees by π180^(∘), we get the corresponding number of radians.

Converting from radian to degrees

If we divide both sides of the equation by π, we get a new equation that describes the number degrees that 1 radian represents. 180^(∘)=π rad ⇔ 180^(∘)/π = 1 rad If we multiply both sides of this equation by an arbitrary number of radians, we can determine how many degrees it is equal to. Let's determine the number of degrees that 6 radians equal.

180^(∘)/π = 1 rad

MultEqn

LHS * 6=RHS* 6

180^(∘)/π * 6= 6 rad

▼

Solve for 6 rad

MoveRightFacToNum

a/c* b = a* b/c

1080^(∘)/π= 6 rad

UseCalc

Use a calculator

343.77467...^(∘) = 6 rad

RearrangeEqn

Rearrange equation

6rad= 343.77467...^(∘)

RoundDec

Round to 2 decimal place(s)

6rad ≈ 343.77^(∘)

As we can see, if we multiply a given number of radians by 180^(∘)π, we get the corresponding number of degrees.