Plane trigonometry, by S.L. Loney.

SINES AND COSINES OF SMALL ANGLES.

337

EXAMPLES. L.
sin 0 1013
1. If a 1014'
prove that 0 is the number of radians in 4~ 24' nearly.
~2. If ~sin 0 863
0 -- 864'
prove that 0 is equal to 4~ 47' nearly.
sin0 _ 5045
0 - 5046'
prove that the angle 0 is 1~ 58' nearly.
sin 0 2165
4, If 2166
0 = - 2166'
prove that 6 is equal to 3~ 1' nearly.
sin f 19493

~, If
5~0." - 19494'
prove that 8 is equal to 1~ nearly.
6. If tan= 5
find an approximate value for 0.
Find the value, when x is zero, of the expressions
x - sin x x2
7. x 8. 1-cosmx
X3 ' 1 - cos mx'
tan x - sin x tan 2x - 2 sin x
10. sin3 ' 11 x3 '
1 m sin x - sin mxc a2 sin ax -
m (cos x - cos mx) b2tan ax -
b2 sin2 ax - a2 sin2 bx 1 x loge (1 -
b2 tan2 ax - a2tan2bx' 1 -cos
ex- 1 +log (1 - ) x + 2 sin.
17. 18.. sin3 x 1* + tan x
sin x + sin 6x - 7x sin2 nx - X
19. X 20. 1- co'
L. T.

sin ax
sin bx. versin ax
versin bx *
- b2 sin bx
- a2tan bx'
~-x)
x
r - sin 3x
- tan 2x
sin2px
spx
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