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MATHMAA

Trigonometric-Functions

In this Trigonometric-Functions you get few formula which are not represented in trigonometric  formula list . You can refer Trigonometric formula by clicking on it . Here few more formula like degrees to radians and vice versa as follows.

Trigonometric-Functions

Relation between Degree and Radian measures:

180$$^{\circ}$$ = $$\prod$$ radians.

Using approximate value of $$\prod$$ = $$\frac{22}{7}$$ we get

1 radian = $$\frac{180^{\circ}}{\prod}$$ =$$57^{\circ}{16}'$$ nearly  and also

$$1^{\circ}$$ = $$\frac{\prod}{180}$$ radian = 0.01746 radian approximately .

1' = 60 "

1$$^{\circ}$$ = 60' ( in words 1 degree = 60 minutes)

1' = $$\frac{1}{60}$$ degree

Examples :

1) Convert the following degrees into radian measure.

a) 30$$^{\circ}$$  b) 45$$^{\circ}$$   c) 60$$^{\circ}$$  d) 75$$^{\circ}$$ e) 90$$^{\circ}$$ f) 120$$^{\circ}$$ g) 135$$^{\circ}$$ h)150$$^{\circ}$$ i) 180$$^{\circ}$$ j) 225$$^{\circ}$$ k) 240$$^{\circ}$$ l) 270$$^{\circ}$$  m) 315$$^{\circ}$$ n) 330$$^{\circ}$$ o)360$$^{\circ}$$

Solutions :

As we know that 1$$^{\circ}$$=$$\frac{\prod}{180}$$ radians .

a) 30$$^{\circ}$$ = 30 * $$\frac{\prod}{180}$$

= $$\frac{\prod}{6}$$

b) 45 $$^{\circ}$$  =  45 * $$\frac{\prod}{180}$$

= $$\frac{\prod}{4}$$

c) 60$$^{\circ}$$ = 60 * $$\frac{\prod}{180}$$

= $$\frac{\prod}{3}$$

d) 75$$^{\circ}$$ = 75 * $$\frac{\prod}{180}$$

= $$\frac{5\prod}{12}$$

e) 90$$^{\circ}$$  = 90 * $$\frac{\prod}{180}$$

= $$\frac{\prod}{2}$$

f) 120$$^{\circ}$$ =120 * $$\frac{\prod}{180}$$

= $$\frac{2\prod}{3}$$

g) 135$$^{\circ}$$ = 135 * $$\frac{\prod}{180}$$

= $$\frac{3\prod}{4}$$

h)150$$^{\circ}$$ = 150 * $$\frac{\prod}{180}$$

=$$\frac{5\prod}{6}$$

i) 180$$^{\circ}$$ = 180 * $$\frac{\prod}{180}$$

= $$\prod$$

j) 225$$^{\circ}$$  = 225 * $$\frac{\prod}{180}$$

= $$\frac{5\prod}{4}$$

k) 240$$^{\circ}$$ = 240 * $$\frac{\prod}{180}$$

= $$\frac{4\prod}{3}$$

l) 270$$^{\circ}$$ = 270 * $$\frac{\prod}{180}$$

= $$\frac{3\prod}{2}$$

m) 315$$^{\circ}$$ = 315 * $$\frac{\prod}{180}$$

= $$\frac{7\prod}{4}$$

n) 330$$^{\circ}$$ = 330 * $$\frac{\prod}{180}$$

= $$\frac{11\prod}{6}$$

o)360$$^{\circ}$$ = 360 * $$\frac{\prod}{180}$$

= 2$$\prod$$

2)  Convert the following radians into degree measures .

a) $$\frac{\prod}{12}$$ b) $$\frac{5\prod}{3}$$ c) $$\frac{2\prod}{5}$$  d)$$\frac{5\prod}{6}$$

Solutions :

As we know that 1 radian = $$\frac{180^{\circ}}{\prod}$$

a) $$\frac{\prod}{12}$$ = $$\frac{180}{12}$$

= 15$$^{\circ}$$

b) $$\frac{5\prod}{3}$$ = $$\frac{5*180}{3}$$

= 300$$^{\circ}$$

c) $$\frac{2\prod}{5}$$ = $$\frac{2 *180}{5}$$

= 72$$^{\circ}$$

d)$$\frac{5\prod}{6}$$ = $$\frac{5*180}{6}$$

=150 $$^{\circ}$$

3) Convert the following into radian measure .

a) 40$$^{\circ}$$20'   b) -47$$^{\circ}$$30'

Solutions :

a) 40$$^{\circ}$$20'

1' = $$\frac{1}{60} ^{\circ}$$

20' = 20 * $$\frac{1}{60} ^{\circ}$$

= $$\frac{1}{3}$$

40$$^{\circ}$$20' = 40+ $$\frac{1}{3}$$

=$$\frac{121}{3}^{\circ}$$

=$$\frac{121}{3}$$* $$\frac{\prod}{180}$$

=$$\frac{121\prod}{540}$$radians

b) -47$$^{\circ}$$30' = -(47 + 30*$$\frac{1}{60} ^{\circ}$$)

= - (47 + 1/2)$$^{\circ}$$

= - $$\frac{95}{2}^{\circ}$$

= - $$\frac{95}{2}$$* $$\frac{\prod}{180}$$ radians

= -$$\frac{19\prod}{72}$$ radians

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