The following material will help you review the important points from Trigonometry that you will need to recall for use in Calculus.

Angles can be measured positively (counterclockwise) or negatively (clockwise) using degrees or radians.

In calculus angles are measured in RADIANS rather than degrees. If you use your calculator at any time you want to make sure that the calculator is in RADIAN MODE!! If when you graph a sine function and it does not appear curved you probably have your calculator in degree mode rather than RADIAN MODE. If an angle A is swept out along a circle, then the size of the angle in radian equals s/r where s is the distance along the circumference of the circle with a radius r.  Recall that , so to convert from degrees to radians or radians to degrees use the equation
 
 

where r is the measure of an angle in radians and d is the measure of an angle in degrees.
 

Check your Understanding: (Remember to write down your answers to these questions.)
 
 1. Let (-3,4) be a point on a circle, as pictured below.  Find the Sin, Cos, Tan, Cot, Sec, and Csc of the red angle
 

There are key trigonometric values which should be memorized. These correspond to the trigonometric functions of the angles defined above. A new chart has been constructed using the unit circle.

Note that some of the function values were positive and others negative and these signs change based on the quadrant. Starting in the first quadrant notice the phrase All Students Take Calculus might help you remember where the sine, tangent, and cosine functions are positive. The figure below indicates where the basic three functions and their reciprocals are positive.
 

Check your Understanding: (Remember to write down the answers to these questions)
1. Make a chart for the sine, cosine, and tangent functions for .

2. Make a chart for the sine, cosine, and tangent functions for the other three quadrants for the matching angles used in question 1.

Converting Between Radian and Degree Measure

Definition of Six Trigonometric Functions