Page 13 - DMTH201_Basic Mathematics-1

Basic Mathematics – I

Notes

Sometimes, it will be necessary to convert from radians to degrees or vice versa. To convert
from degrees to radians, multiply by (( )/180 ). To convert from radians to degrees, multiply by
(180 /( )).

1.3 Sines and Cosines Defined
Sine and cosine are periodic functions of period 360°, that is, of period 2 . That’s because sines

and cosines are defined in terms of angles, and you can add multiples of 360°, or 2 , and it
doesn’t change the angle.

Properties of Sines & Cosines following from this definition
There are numerous properties that we can easily derive from this definition. Some of them

simplify identities that we have seen already for acute angles.
Thus,
sin (t + 360°) = sin t, and
cos (t + 360°) = cos t.
Many of the current applications of trigonometry follow from the uses of trig to calculus,
especially those applications which deal straight with trigonometric functions. So, we should use
radian measure when thinking of trig in terms of trig functions. In radian measure that last pair
of equations read as:

sin (t + 2 ) = sin t, and
cos (t + 2 ) = cos t.
Sine and cosine are complementary:
cos t = sin ( /2 – t)

sin t = cos ( /2 – t)

We’ve seen this before, but now we have it for any angle t. It’s true because when you reflect the
plane across the diagonal line y = x, an angle is exchanged for its complement.

The Pythagorean identity for sines and cosines follows directly from the definition. Since the
2
point B lies on the unit circle, its coordinates x and y satisfy the equation x + y = 1. But the
2
coordinates are the cosine and sine, so we conclude
2
sin t + cos t = 1.
2

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