Plane trigonometry, by S.L. Loney.

172

TRIGONOMETRY.

[Exs. XXV.]

3. Given cosec 65~ 24'= 10998243,
diff. for 1'= 1464,
find the value of cosec 65~ 24' 37"
and the angle whose cosec is 1-0997938.
4. Given L tan 22~ 37' = 9-6197205,
diff. for 1'=3557,
find the value of L tan 22~ 37' 22"
and the angle whose L tan is 9-6195283.
5. Find the angle whose L cos is 9-993, given
L cos 10~ 15'= 9-9930131, diff. for 1'= 229.
6. Find the angle whose L sec is 10-15, given
L sec 44~ 55'= 10'1498843, diff. for 1'= 1260.
7. From the table on page 170 find the values of
(1) L sin 32~ 18' 23", (2) L cos 32~ 16' 49",
(3) L cot 32 29' 43", (4) L sec 32~ 52'27",
(5) L tan 57~ 45' 28", (6) L cosec 57~ 48' 21",
and (7) L cos 57~ 58' 29".
8. With the help of the same page solve the equations
(1) Ltan 0=10-1959261, (2) Lcosec 0=10-0738125,
(3) L cos O=9-9259283, and (4) L sin =9 9241352.
9. Take out of the tables L tan 16~ 6' 23" and calculate the value of
the square root of the tangent.
10. Change into a form more convenient for logarithmic computation
(i.e. express in the form of products of quantities) the quantities
(1) 1+tan x tany, (2) 1 - tan x tany,
(3) cot x+ tany, (4) cot x-tany,
1 - cos 2x d tan x + tan y
1 + cos 2x' and cot x + cot y