Intro to Calculus March 2010

The trigonometric functions are among the most fundamental in mathematics. They were initially developed to aid in the measurement of triangles and their angles, and they are used daily in surveying and navigation. However they can be used to describe any natural phenomenon that is periodic, and in higher mathematics they are fundamental tools for understanding many abstract spaces.

 The primary use of trigonometric functions is in the measurement of angles. Although the ancient Babylonian degree unit of angle measure is still in wide use, in mathematics we prefer to use the radian measure. Given a circle centered at the origin in the Cartesian plane, imagine taking a radius and laying it along the outside circle, beginning at the x axis and going counterclockwise.Cartesian plane

 We begin with two basic measurements followed by two fundamental definitions.  Once around a circle is 360º.  And that the circumference of a circle is 2r

Using the fact that 360º corresponds to 2Π radians, we can generate the following angle measures: Dividing equals 180º which is radians Dividing gives us 90º which is radians

Using the fact that 360º is 2 radians and 180º is radians, we can always convert degrees to radians by Multiplying thedegree measurement by

If we have a radian measure we can multiply by So

Degree measure of angle is based upon the in a circle and radian measure is based upon as another way to describe one complete circle. We can convert from radians to degrees And from degrees to radians.

rad 34º 4π rad 46º rad 3π rad π rad 150º rad 732º 6π rad rad 2010º Convert to radians or degrees!

Convert to radians 52º 34º 35º 4π rad 74º 36º 15º 37º 94º 53º 174º 156º 376º 324º 163º 532º 272º 631º 856º 428º 732º 994º 897º 1768º 2000º

Convert to degrees 2π rad π rad 3π rad 4π rad 7π rad 9 rad 4π rad π rad 14π rad 8π rad 3π rad 25π rad 45π rad 6π rad 73π rad 8 rad 2π rad 6π rad 5π rad 3π rad