MATHEMATICS O LEVEL(FORM TWO) NOTES – TRIGONOMETRIC TABLES

Trigonometric Tables

Trigonometric tables provide values of sine, cosine, and tangent for angles, typically prepared to four decimal places.

How to Read the Value of Trigonometric Angles from Mathematical Tables

Example 1

Find the value of the following using mathematical tables:

• Sin 43° = 0.6820
• Sin 58° = 0.8480
• Sin 24°42′ = 0.4179
• Sin 52°26′ = 0.7923 + 0.0004 = 0.7927

Example 2

Using mathematical tables, evaluate the following:

• Cos 37° = 0.7986
• Cos 82° = 0.1392
• Cos 71°34′ = 0.3162
• Tan 20° = 0.3640
• Tan 68° = 2.4751
• Tan 54°22′ = 1.3950

Example 3

Find the value of the following angles from trigonometric ratios:

• Sin p = 0.6820
  p = Sin^-1(0.6820)
  p = 43°
• Sin Q = 0.7291
  Q = Sin^-1(0.7291)
  Q = 46°48′
• Tan R = 5.42
  R = Tan^-1(5.42)
  R = 79°33′

Application of Sine, Cosine, and Tangent Ratios in Solving a Triangle

Sine, cosine, and tangent ratios are used to find unknown side lengths in triangles.

Example

From the table:

Sine C =

Sin 55° =

20 × Sin 55° = x

20 × 0.8198 = x

x = 16.4 cm

The value of x is 16.4 cm.

Example 2

Find the length XY in triangle XYZ.

Solution:

From the table:

tan 62° =

tan 62° =

13 × tan 62° = XY

13 × 1.8807 = XY

XY = 24.4 cm

Example

Evaluate the value of m and give your answer to 3 decimal places.

From the table:

Cos R =

Cos 36° =

m =

m =

m = 14.833 cm

The value of m is 14.833 cm.

Exercise

Solution:

From the table:

tan 43° =

tan 43° =

17 × tan 43° = y

y = 17 × 0.9325

y = 15.85 cm