Plane trigonometry, by S.L. Loney.

TRIGONOMETRICAL RATIOS.

29

Ex. 3. If cos 0 equal, find the values of the other ratios.
Along the initial line OA take OM equal to 3, and erect a perpendicular MP.
Let a line OP, of length 5, revolve round 0 until its other end meets
this perpendicular in the point P. Then AOP is the angle 0.
By Euc. i. 47, iMP=, OP - OM2= /5232= 4.
Hence clearly
sin 0=, tan0=, cot 0=, cosec0= and sec0=.
5 3 4 4 3
Ex. 4. Supposing 0 to be an angle whose sine is, to find the numeri3
cal magnitude of the other trigonometrical ratios.
Here sin 0=3, so that the relation (2) of Art. 27 gives
(1+ os2 0=1,
9-9'
i.e. cos 0= 29 2
3
sin 0 1 _ /2
Hence tan = =
cos0 —2J/2- 4 '
cot 0= - 2an -2,
tan O
cosec 0= s-i = 3,
sin 0
1 3 3^/2
sec 0= -- -
cos 0 2/2- 4
vers = 1 - cos 0=1- 22
3,
1 2
and covers 0=1- sin 0 =1 - -
3 3