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Right Triangle Trigonometry Part 2

Updated on May 31, 2009

Sine, Cosine and Tangent

Sine, Cosine and Tangent are three trigonometric functions. Each of these functions describes the ratio associated with a given angle, as a numeric value. Sine describes a ratio of the length of the side opposite an angle to the length of the hypotenuse of the triangle. Cosine describes a ratio of the length of the side adjacent to an angle to the length of the hypotenuse of the triangle. Tangent describes a ratio of the length of the side opposite an angle to the length of the side adjacent to the angle.

Fig. 1 - Right Triangle
Fig. 1 - Right Triangle

Six Trigonometric Ratios

The following six ratios will describe the triangle pictured in Fig. 1

  • The sine of angle 1 is equal to the ratio of opposite side C to the hypotenuse B
  • The cosine of angle 1 is equal to the ratio of adjacent side A to the hypotenuse B
  • The tangent of angle 1 is equal to the ration of opposite side C to the adjacent side A
  • The sine of angle 2 is equal to the ratio of opposite side A to the hypotenuse B
  • The cosine of angle 2 is equal to the ratio of adjacent side C to the hypotenuse B
  • The tangent of angle 1 is equal to the ration of opposite side A to the adjacent side C

Fig. 2 - Right Triangle
Fig. 2 - Right Triangle

Six Trigonometric Ratios

Referencing the triangle in Fig. 2, values will now be used to describe the relationships of the sides and angles.

  • The sine of angle 1 is equal to 6:10 or 0.60 (6/10)
  • The cosine of angle 1 is equal to 8:10 or 0.80 (8/10)
  • The tangent of angle 1 is equal to 6:8 or 0.75 (6/8)
  • The sine of angle 2 is equal to 8:10 or 0.80 (8/10)
  • The cosine of angle 2 is equal to 6:10 or 0.60 (6/10)
  • The tangent of angle 2 is equal to 8:6 or 1.33 (8/6)

The numeric values associated with angles 1 and 2 can now be used to find the actual size of the angles. Up to this point, angles 1 and 2 have not been assigned an angular value. All that is known about the size of the angles is that they must have a sum of 90°. Remember, that the sum of all the angles must be 180°. Since one of the angles remains 90°, angles 1 and 2 comprise the difference (90°).

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