1.6a day 1 Evaluating Trig Functions Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 2008 Church of St. Mary, by Sir Christopher Wren, London, England 1672 now at the National Churchill Museum, Westminster College Fulton, Missouri

When you were first introduced to trigonometry, trig functions were defined in terms of the sides of a right triangle. opposite hypotenuse adjacent If we superimpose this triangle on a unit circle, we can redefine the functions in terms of x and y.

Using these definitions, we can evaluate trig functions for angles on the x and y axis that do not make a triangle.

A sine curve is just the graph of the y values of a unit circle as the angle changes: This means that we can use a unit circle to evaluate the sine function. All we have to do is find the y values! (A unit circle has a radius of 1.)

The sine of an angle is the y- value (vertical distance). If you forget, sine is vertical, like a stop sign!

The cosine of an angle is the x-value (horizontal distance).

Once you know sine and cosine, you can find the other functions using the definitions: Functions are undefined when the denominator is zero.

Now lets try a few. Answer as quickly as you can!

Now lets try a few. Answer as quickly as you can!

Now lets try a few. Answer as quickly as you can!