Name: _____________________________________________ Date: ___________________________

PreCalc – Special Right Triangles on a Coordinate Plane

Where appropriate in the questions below, rationalize your answers. Write the ratios of the trigonometric functions into the table in WS 0-360 Special Right Triangles.

For Questions 1-4 use Figure 1.

Write the lengths of the sides of all triangles onto the diagram. If the sides are not in Quadrant I, note which sides are negative.

1. In Quadrant I, a. Determine and write the in the space provided. b. Find the values of the sine, cosine, and tangent trigonometric functions. Rationalize your answers and

enter them into the 0-360 table which is on a separate worksheet.

Figure 1

2. In Quadrant II, find . In this quadrant, . Use the triangle in Quadrant II to find the ratios of the sine, cosine, and tangent trigonometric functions. Write your answers into your table.

3. In Quadrant III, find . In this quadrant, . Use the triangle in Quadrant III to find the ratios of the sine, cosine, and tangent trigonometric functions. Write your answers into your table.

4. In Quadrant IV, find . In this quadrant, . Use the triangle in Quadrant IV to find the ratios

of the sine, cosine, and tangent trigonometric functions. Write your answers into your table.

1

0.8

0.6

0.4

0.2

-0.2

-0.4

-0.6

-0.8

-1

-1.5 -1 -0.5 0.5 1 1.5

A

𝑚 𝐴𝐹𝐵 ______________ B

𝑚 𝐴𝐹𝐶 ______________ C

𝑚 𝐴𝐹𝐷 ______________ D

𝑚 𝐴𝐹𝐸 ______________ E

Note: F = (0,0) F

1.5

1

0.5

-0.5

-1

-1.5

-1 1

= 60

B

D

A

In each Quadrant: find and label all sides of the triangles with their lengths. Then calculate the measures of the angles. Use these values to determine the values of the sine, cosine, and tangent trigonometric functions for that angle. Rationalize your answers and enter them into the 0-360 table which is on a separate worksheet.

Hint: lengths of some sides will be NEGATIVE.

For Questions 5-8 use Figure 2. 5. In Quadrant I

6. In Quadrant II

______________ 7. In Quadrant III

______________

8. In Quadrant IV ______________

For Questions 9-12 use Figure 3.

9. In Quadrant I

______________ 10. In Quadrant II

______________

11. In Quadrant III ______________

12. In Quadrant IV ______________

1

0.5

-0.5

-1

-2 -1 1 2

= 30

Figure 2

Figure 3

B C

D E

A F

A

B C

D E

F