# Trig Functions Applet Worksheet

The first set of exercises look at the definitions of the trig functions, connecting the various ways that the functions can be defined.
1. Start with the sine function.  (Click the "Show sin and cos" button.  Find all the things on the worksheet that are displayed in red.)
• Repeat the definition of sin that is a ratio of sides of a right triangle.  (Use adj, opp, and hyp.)
• Give the vertices of the triangle centered at the origin that has a red side.  Note that the side in the denominator of the definition of sine has length 1 in this triangle.
• If the red side uses the normal conventions for positive and negative, in which quadrants do you expect sine to be positive?
2. Repeat exercise 1 with the cosine function.  (Use orange rather than red.)
3. Now consider the tangent Function.  (Click the "Hide sin and cos" and "Show sec and tan" buttons.  The value of tangent is tan colored.  Find the corresponding line segment and value.)
• Repeat the definition of tan that is a ratio of sides of a right triangle.  (Use adj, opp, and hyp.)
• Give the vertices of the triangle centered at the origin that has a tan side.  Note that the side in the denominator of the definition of sine has length 1 in this triangle.  (Note that the tangent is the length of a segment on a line tangent to the circle.)
• What can you say about the quadrants where tan is positive and negative?
4. For the secant function we use the same triangle as the tangent function, but look at a brown side.
• Repeat the definition of sec that is a ratio of sides of a right triangle.  (Use adj, opp, and hyp.)
• Notice that the secant is positive or negative in the same quadrants where cosine is positive or negative.
• If the brown side uses the normal conventions for positive and negative, in which quadrants do you expect sec to be positive?
5. Repeat exercise 3 with the cot function.  (Click "Show cot and csc" and appropriate "Hide ..." buttons.  Use dark blue as a color and the co-tangent line.)
6. Repeat exercise 4 with the cos function.  (Use light blue.)
7. As accurately as you can fill in the table below:
 Angle = theta sin(theta) cos(theta) tan(theta) 30 degrees 3/2 pi radians 1 radian 45 degrees