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Geometry Session 8, Part C: Trigonometry
 
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Session 8, Part C:
Trigonometry

In This Part: Right Triangle Ratios | Trigonometric Functions

As you've seen, the trigonometric functions such as sine, cosine, and tangent are nothing more than ratios of particular sides in right-angle triangles. Note 8 These ratios depend only on the measure of an angle and have special names:

In the triangle above, the sine of angle A is defined as BC/AB. It is abbreviated sin A.

The cosine of angle A is defined as AC/AB. It is abbreviated cos A.

The tangent of angle A is defined as BC/AC. It is abbreviated as tan A. Note 9

Use the Interactive Activity to answer Problem C3 and C4 and to experiment with the trigonometric functions. For example, how big can sine get? What about cosine? How do you make them as big as possible? What about tangent? Does it seem to have a maximum value?

This activity requires the Flash plug-in, which you can download for free from Macromedia's Web site.

 

Problem C3

Solution  

For the original triangle:

a. 

Find sin A and cos A.

b. 

Find sin B and cos B.


 

Problem C4

Solution  

For the following triangle:

a. 

Find sin A and cos A.

b. 

Find sin B and cos B.

c. 

Find tan A and tan B.


 

Problem C5

Solution  

a. 

Find sin 30°, cos 30°, and tan 30° in the triangle below. Then find sin 60°, cos 60°, and tan 60°.

b. 

Find sin 45°, cos 45°, and tan 45° in the triangle below.


 

Problem C6

Solution  

Suppose you have any right triangle ABC (with the right angle at C). Explain why it must be true that sin A = cos B.

 

Problem C7

Solution  

Most public buildings were built before wheelchair-access ramps became widespread. When it came time to design the ramps, the doors of buildings were already in place. Suppose a particular building has a door two feet off the ground. How long must a ramp be to reach the door if the ramp is to make a 10° angle with the ground? (This is why so many access ramps must make one or more turns!)

sin 10° 0.17 and cos 10° 0.98 Note 10


 

Problem C7 taken from Connected Geometry, developed by Educational Development Center, Inc. p. 341. © 2000 Glencoe/McGraw-Hill. Used with permission. www.glencoe.com/sec/math

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