Sine and Cosine Ratios Table and Calculator Use

Lesson 2: The Sine and Cosine Ratios - Sine and Cosine Ratios Table and Calculator Use

   Constructing Knowledge

In Lesson 1, you saw that a table of tangent ratios could be made and used to solve right angle triangle problems. The following table shows the tangent, sine, and cosine ratios for various angle measures. All values are approximate, rounded to the nearest hundredth (or thousandth).

θ	tan θ	sin θ	cos θ
5°	0.09	0.09	0.996
10°	0.18	0.17	0.98
15°	0.27	0.26	0.97
20°	0.36	0.34	0.94
25°	0.47	0.42	0.91
30°	0.58	0.5	0.87
35°	0.70	0.57	0.82
40°	0.84	0.64	0.77
45°	1	0.71	0.71
50°	1.19	0.77	0.64
55°	1.43	0.82	0.57
60°	1.73	0.87	0.5
65°	2.14	0.91	0.42
70°	2.75	0.94	0.34
75°	3.73	0.97	0.26
80°	5.67	0.98	0.17
85°	11.43	0.996	0.09

Again, use of the table is limited to problems involving the angle measures and ratios listed. Alternatively, the sin, sin^-1, cos, cos^-1, tan, and tan^-1 functions on a calculator can be used with any ratio or angle measure.

Correctly entering ratios and determining angles using the trigonometry functions on a calculator is an important skill in this chapter. Attempt Example 1 with your calculator to ensure you are using the correct key sequences.

EXAMPLE 1

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Use a calculator to determine the value of y in each of the following equations. Express angle measures to the nearest degree, and ratios to the nearest hundredth.

1. sin 23° = y


2. cos 23° = y


3. sin y = 0.54 (to calculate for an angle measure use the sin^-1 key on your calculator)


4. cos y = 0.13 (to calculate for an angle measure use the cos^-1 key on your calculator)

Solution

1. sin 23° = y
   y = 0.390...
   y = 0.39


2. cos 23° = y
   y = 0.9205...
   y = 0.92


3. sin y = 0.54 (to calculate for an angle use the sin^-1 key on your calculator)
   y = 32.683...
   y = 33°


4. cos y = 0.13 (to calculate for an angle use the cos^-1 key on your calculator)
   y = 82.530...
   y = 83°

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