9* The same in terms of the suyersedsine, (or rersed-
sine of the supplement.)

10. If tan0 + cot 9 = m, express all the trigonometri-
cal functions in terms of iit.
11. Find sin from the equation sin 9 cos = m.
12. If the right angle were divided into 100® instead of
90^, what would be the value of an angle of S6^ 7' ?



TEIGONOMETBT. 47

IS. Determine the number of degrees into which the
riglit angle must be divided in order that an angle of S(fi
may be measured by the number 40.
14. Shew that as the angle increases each of the
trig^onometrical functions changes sign whenever it passes
through the value or oo , and for no other value.
FORMULJE INVOLVING FUNCTIONS OF ONE ANGLE.
!• Prove the following formula :
sind = sin {{2n + J) 180* - ^} = - sin {(2n + 1)180* + 9\

« - sin {(2n + 2)180* - 0],
cos (360* - 0) = - cos (180* + 6),
sin (90* + 0) = sin (90* - 0),
tan0 = - tan (180* - 0) - - tan {(2n + 1) 180* - 0],
= tan (180* + 0) = tan {{2n + 1) 180* + 0},
cosec = cosec {(2n + i) 180* - 0\,
sec « sec (- 0) « sec (n . s6o* - ff),
sin + cos + tan - sec = 0, when = 180*,
sin e cot 6 = 1, when 0^0,

sin - cos = 0, when = 45*,

sin + cos = 0, when = 1S5*.
2. If tan30 = -, then--^ + -v^x.(a? + fc¥.
