Plane Trigonometry

Cover Plane Trigonometry
Plane Trigonometry
R D Rosser Daniel Bohannan
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/. Sin (-0) = - sin0, sin t-A°) = - sin A°.
63] THE SINE FAMILY.
97 (iii) Any angle of a terminal has the opposite sine of any angle of the opposite terminal.
sin \ (2 n + 1) ir + 0\ = - sin (2 mir + 0), or, sin j (2 n + 1) 180° + A°\ = - sin A% where m, w are any positive or negative integers.
-£*- "7 y s *t- y * -i y y o i l -+ -fe «^ * r i ?
jzL ^f£ Fig. 26.
^ \ . 1/ iT\ Fig. 28.
Fig. 29.
X A ^■^^ ^^\ ''j -M ^ v ».
^2 ^"-^ ^^\^ ""• ^ ?- Fig. 27.
2j "* _5k ^ -S* *r- if - ^- — ~2 ::e. J .. -*:
... ■ 4- ^ ■ ' "P -T *t (iv) Any angle of any terminal has the opposite sine of any angle of the terminal symmetric to the horizontal.
sin (2 nir + 0) = — sin (2 mir — 0), sin (2 n • 180 + A°) = - sin (2 m 180° - A ), where m, w. Are any positive or negative integers.
98 PLANE TRIGONOMETRY. [§63 (v) Thus, while adding an angle in degree measure to an even multiple of 180° or subtracting it from any odd mul- tiple of 180° leaves the sine unchanged, the reverse changes the sign of the sine.


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