Plane trigonometry, by S.L. Loney.

ANGLES OF ANY SIZE.

63

MISCELLANEOUS EXAMPLES. IX.
1. In a triangle one angle contains as many grades as another contains degrees, and the third contains as many centesimal seconds as
there are sexagesimal seconds in the sum of the other two; find the
number of radians in each angle.
2. Find the number of degrees in the angle at the centre of a circle
whose radius is 5 feet which is subtended by an arc of length 6 feet.
3. To turn radians into seconds prove that we must multiply by
206265 nearly, and to turn seconds into radians the multiplier must be
*0000048.
4, If sin 0 equal x y2+, find the values of cos 0 and cot 0.
4. I sin equalx2+y2,
5. If sin0= -2+ 2nin
-59 If 0 ~17m2 + 2nn + 2n2 '
mii2 ~ 2rnn
prove that tan 08 2n + 2n2'
6. If cos 0- sin 0=-/2 sin 0,
prove that cos 0 + sin 0 =,/2 cos 0.
7. Prove that
cosec6 a - cot6 a = 3 cosec2 a cot2 a + 1.
8. Express 2 sec2 A - sec4 A - 2 cosec2 A + cosec4 A
in terms of tan A.
9. Solve the equation 3 cosec2 0=2 sec 0.
10. A man on a cliff observes a boat at an angle of depression of
30~, which is making for the shore immediately beneath him. Three
minutes later the angle of depression of the boat is 60~. How soon will
it reach the shore?
1,
11. Prove that the equation sin 0=x +- is impossible if x be real.
X
4xy
12. Shew that the equation sec2 0 = (+y)2 is only possible when
As-==?.