This is an introduction to trigonometry, which is a key concept you will use in calculus next year. We will
be dealing right triangles and the ratios of right triangles.
1. First, open the file which has been emailed to you; it has been named Noyce.
2. Notice that there is a circle. What is the radius of the circle?
Can you write the equation of the circle?
3. In trigonometry, we call the x-axis cosine and the y-axis sine. We shorten the names to sin and cos.
With this information, how could you rewrite the equation of the circle?
4. What is the max and min of sin and cos? Where does this occur? Fill these values in the chart below.
5. Notice that there is a right triangle within the circle. Move B so that you have a 30 degree angle,
what are the values of sin and cos? 45 degree angle? 60 degree angle?
6. With the circle below, fill in your (x, y) coordinates with what you have found. Please stay in the first
quadrant. Can you guess what the rest of the circle might be? Fill it in with your answers.
HINT! Round values and…
Use
Use
√3
2
√2
2
in the chart for .87
in the chart for .71
Use ½ in the chart for .5
(0 ,1)
(
,
)
( , )
60⁰
45⁰
30
⁰
(
,
)
( 1 , 0)