Plane trigonometry, by S.L. Loney.

A
RATIOS OF - IN TERMS OF SIN A. 123
e n tan7r +A (2p+ 1)7r + A
Then tan. = tan
2 2
= tan 7pr + 7 A) = tan (Art. 84)
=-cot 2. (Art. 70.)
A
Hence the formula which gives us the value of tan -
A
should be expected to give us also the value of - cot.
An illustration of this is seen in the example of the
last article.
EXAMPLES. XVIII.
1 1
1. If sin 0= 2 and sin =, find the values of sin (0 + 5) and
sin (20 + 20).
2. The tangent of an angle is 2-4. Find its cosecant, the cosecant of
half the angle and the cosecant of the supplement of double the angle.
11 42
3. If cosa=- and sin3=-, find the values of sin and
~61 /3~ and
cos2 a+ the angles a and 3 being positive acute angles.
24
4. If cosa=3 and cos p=4, find the value of cos -, the angles
o5 2
a and p being positive acute angles.
5. Given sec 0 = 1~, find tan and tan 0.
6. If cos A ='28, find the value of tan 2, and explain the resulting
ambiguity.
7. Find the values of (1) sin 71, (2) cos 7~, (3) tan 221~, and
(4) tan 110.