Exercise 110 Page 600

Practice makes perfect

In order to convert from a given number of degrees to its corresponding radians, we will use the following relationship.

18 0^{\circ} = π radians

Notice that we can divide both sides by

18 0^{\circ}

to fin how many radians

1^{\circ}

represents.

1^{\circ} = \frac{π}{1 8 0} radians

Now, we can convert the given number of degrees to radians if we multiply both sides by

30 .

1^{\circ} = \frac{π}{1 8 0} radians

MultEqn

$LHS \cdot 30 = RHS \cdot 30$

3 0^{\circ} = \frac{π}{1 8 0} \cdot 30 radians

MoveRightFacToNum

$\frac{a}{c} \cdot b = \frac{a \cdot b}{c}$

3 0^{\circ} = \frac{3 0 π}{1 8 0} radians

ReduceFrac

$\frac{a}{b} = \frac{a / 3 0}{b / 3 0}$

3 0^{\circ} = \frac{π}{6} radians

Let's repeat the procedure from Part A.

1^{\circ} = \frac{π}{1 8 0} radians

MultEqn

$LHS \cdot 15 = RHS \cdot 15$

1 5^{\circ} = \frac{π}{1 8 0} \cdot 15 radians

MoveRightFacToNum

$\frac{a}{c} \cdot b = \frac{a \cdot b}{c}$

1 5^{\circ} = \frac{1 5 π}{1 8 0} radians

ReduceFrac

$\frac{a}{b} = \frac{a / 1 5}{b / 1 5}$

1 5^{\circ} = \frac{π}{1 2} radians

Again, let's repeat the procedure we established in previous Parts.

1^{\circ} = \frac{π}{1 8 0} radians

MultEqn

$LHS \cdot (- 75) = RHS \cdot (- 75)$

- 7 5^{\circ} = \frac{π}{1 8 0} \cdot (- 75) radians

MultPosNeg

$a (- b) = - a \cdot b$

- 7 5^{\circ} = - \frac{π}{1 8 0} \cdot 75 radians

MoveRightFacToNum

$\frac{a}{c} \cdot b = \frac{a \cdot b}{c}$

- 7 5^{\circ} = - \frac{7 5 π}{1 8 0} radians

ReduceFrac

$\frac{a}{b} = \frac{a / 1 5}{b / 1 5}$

- 7 5^{\circ} = - \frac{5 π}{1 2} radians

Like in previous parts, we will repeat the established procedure.

1^{\circ} = \frac{π}{1 8 0} radians

MultEqn

$LHS \cdot 630 = RHS \cdot 630$

63 0^{\circ} = \frac{π}{1 8 0} \cdot 630 radians

MoveRightFacToNum

$\frac{a}{c} \cdot b = \frac{a \cdot b}{c}$

63 0^{\circ} = \frac{6 3 0 π}{1 8 0} radians

ReduceFrac

$\frac{a}{b} = \frac{a / 9 0}{b / 9 0}$

63 0^{\circ} = \frac{7 π}{2} radians

Subchapter links

11.2.1 Creating a Three-Dimensional Model p.582-583

11.2.2 Graphing Equations in Three Dimensions p.586-587

11.2.3 Solving Systems of Three Equations with Three Variables p.590-592

11.2.4 Using Systems of Three Equations for Curve Fitting p.598-600

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