# Arithmetic Formulas Examples And Worksheet With Answer Key - Dr. Neal, Wku

Dr. Neal, WKU
MATH 117
Arithmetic Formulas
Given angles A and B , there several important arithmetic formulas for the sine and
cosine of the angles A ± B , as well as angles such as ! A , 90º ! B , 2 A , and B / 2 . In each
case, we can obtain an exact formula for the result in terms of the sine and cosine of the
original angles A and B without knowing the actual values of the angles A and B .
Negative Angles
Because angles A and ! A create the same x -
coordinates on the unit circle, but negative y -
(x , y)
coordinates, we have
cos A = cos(! A)
A
! A
and
sin(! A) = ! sin A
(x ,! y)
Complimentary Angles
Because the x and y values are switched for
(y, x )
complimentary angles such as 30º and 60º, we have
sin(90 º ! A) = cos(A)
90º ! A
(x , y)
and
A
cos(90º ! A) = sin(A)
A
Supplementary Angles
Because supplementary angles, such as 30º
and 150º, have the same y -coordinates but
180º ! A
negative x -coordinates, we have
(! x, y)
(x , y)
sin(A) = sin(180º ! A)
A
A
and
cos(180º ! A) = ! cos( A)