Plane trigonometry, by S.L. Loney.

ANGLES HAVING A GIVEN COSINE.

77

78. To construct the least positive angle whose cosine
is equal to b where b is a proper fraction.
Along the initial line measure off a distance OMA equal
to b and draw AMP perpendicular to OA.
[If b be negative M will lie on the other
side of 0 in the line AO produced.]
With centre 0 and radius equal to M ^
unity, describe a circle and let it meet
MP in P.
Then AOP is the angle required. For _ ' P
0M b
cos AOP = O = = b.
79. To construct the least positive angle whose tangent
is equal to c.
Along the initial line measure off
OM equal to unity and erect a per- c
pendicular /]IP. Measure off' MP
equal to c. 0 1 M A
Then
tan AOP =c
so that AOP is the required angle.
80. It is clear from the definition given in Art. 50,
that, when an angle is given, so also is its sine. The
converse statement is not correct; there is more than one
angle having a given sine; for example, the angles 30~,
150~, 390~, - 210~,... all have their sine equal to 2.
Hence, when the sine of an angle is given, we do not
definitely know the angle; all we know is that the angle
is one out of a large number of angles.