Download Accelerated Math 3

Gifted/ Accelerated Math 3
Trigonometry & The Unit Circle
Name: _______________________
Date: _______________________
Right Triangle Review
SOH – CAH – TOA
Special Right Triangles
Find the missing lengths on each triangle.
1.
2.
3.
60
c
b
18
c
16
30 
4 3
30
a
45 
45 
Constructing a Unit Circle
Supplies:
 4 different colors of paper
 A pencil & a pen or a marker
 Ruler
 Protractor
 Compass
 Scissors
 Glue
1. Using the paper provided, a straight edge, and a protractor draw a 30-60-90 and a 45-45-90
triangle. The hypotenuses of the two triangles must be the same length – anywhere
between 3 & 4 inches. Choose three different colors of paper and use these triangles as a
pattern to produce 8 30-60-90 triangles and 4 45-45-90 triangles. Four of the 30-60-90
triangles should be on the 1st color and four the 2nd color. The 4 45-45-90 should be made with
the 3rd color of paper.
2. Label the length of the hypotenuse 1, to indicate that its length is 1 unit. Label the other sides
of the triangles using the appropriate ratios for the lengths of the sides of a 30-60-90 and 4545-90 triangles. (Label this in pencil for now, when you finish the assignment go back over
the measurements with pen or a marker.)
3. Use a compass to draw a circle (centered on the page) with a radius that is the same length as
the hypotenuse of the triangles on the 4th sheet of paper.
4. With the center of the circle as the origin, draw a pair of coordinate axes. The horizontal x-axis
and the vertical y-axis must be perpendicular.
5. DO NOT GLUE ANYTHING UNTIL STEP 10: Place 4 of the same color 30-60-90 triangles on
the circle with the vertex of the 30o angle at the origin. All four triangles should be placed so
that their reference angle is 30o. For the 300 reference angle the longer leg of each triangle
should be lined up with the x-axis. Label the angle formed and the point where the
segment intersects the circle with x and y coordinates which are the lengths of
the legs of the triangle on the outside of the circle.
6. Repeat this process using the 2nd color of 30-60-90 triangles and place the 60o angle at the
origin of the circle.
7. Repeat this process using the 45-45-90 triangles.
8. Now that all triangles have been placed onto your unit circle, stagger the order (i.e. in one
quadrant place the 30o reference angle on top, in another place the 45o reference angle on top,
and in another place the 60o reference angle on top).
9. Make sure that all angles and points visible are labeled in pen or marker.
10. After finishing the Unit Circle compare it with other students’ circle. Resolve any differences.
Glue the triangles onto your circle.