SMART Packet #6
Basic Trigonometric Ratios
Student: / Teacher:Standards
A.A.42 Find the sine, cosine, and tangent ratios of an angle of a right triangle, given the lengths of the sides
What is a trigonometric ratio?
It is a fraction that is used to “measure” a right triangle.
These fractions always use two sides of the triangle.
EXAMPLE
Here are six ratios that you can write using the sides of this triangle:
Practice (Part I)
1. Write six ratios using the sides of the triangle below.
2. Write six ratios using the sides of the triangle below.
What are the three trigonometric ratios?
The three basic trigonometric ratios are sine, cosine, and tangent.
We usually write these as: SIN COS and TAN
Example: Writing a SIN ratio
Identify the angle first!
Label the three sides.
SIN is
Practice: Writing a SIN ratio
Identify the angle first!
Label the three sides.
SIN is
Practice: Writing a COS ratio
Identify the angle first!
Label the three sides.
COS is
Practice: Writing a TAN ratio
Identify the angle first!
Label the three sides.
TAN is
Practice (Part III)
3. Which of the following statements are correct? Choose all that apply.
4. Which of the following represents the ratio for ?
a.
b.
c.
d.
5. Write a ratio for .
6. Write a ratio for .
7. Write a ratio for .
8. Which ratio is correct for angle x ?
a.
b.
c.
9. Which of the following represents the ratio for ?
a.
b.
c.
d.
10. Which of the following represents the ratio for ?
a.
b.
c.
d.
11. Which ratio represents in simplest form ?
(See the hint on problem #10.)
a. c.
b. d.
12. Write as a reduced fraction. (See the hint on problem #10.)
13. Circle all of the triangles that would use a cos ratio.
14. Graph and label the following points on the coordinate plane below:
A(1, 3) B(5, 3) C(5, –6)
Connect the points to form a right triangle.
Then write the ratios below.
15. Graph and label the following points on the coordinate plane below:
A(–4, 5) B(–4, –7) C(3, 5)
Connect the points to form a right triangle.
Then write the ratios below.
16. Graph and label the following points on the coordinate plane below:
A(–6, 0) B(–6, –6) C(0, –6)
Connect the points to form a right triangle.
Then write the ratios below.