Sine Cosine Tangent Formula

Sine Cosine Tangent Formula

The fundamental trigonometric ratios used to analyse how a triangle’s angles and sides relate are the Sine Cosine Tangent Formula (especially of a right-angled triangle). Hipparchus used the principles of Trigonometry to establish the relationship between the sides and angles of a right triangle, whereas Pythagoras focused on the relationship between a right triangle’s sides through the Pythagorean theorem. A right-angled triangle’s missing sides or angles can be found using the trigonometric Sine Cosine Tangent Formula.

The three fundamental trigonometric ratios, namely the Sine Cosine Tangent Formula, each yield the ratio of the lengths of the two sides of a right-angled triangle. Students must be aware that the three sides of a right-angled triangle are called the “legs” and the “hypotenuse,” respectively. Thus, the longest side of a right-angled triangle is still referred to as the “hypotenuse” in Trigonometry, while the other two legs are referred to as the “opposite side” and “adjacent side.” Based on the angle students are discussing, they should determine the “opposite” and “adjacent” sides.

  • The side that is directly “opposite” to the angle is known as the “opposite side” or the perpendicular.
  • The side that “touches” the angle (other than the hypotenuse) is referred to as the “near side” or the base.

Formulas for Sine, Cos, Tan

In Trigonometry, the terms “Sine Cosine Tangent Formula” denote the values of the corresponding trigonometric functions for the specified angle. By determining the necessary side ratio, students can get the Sine Cosine Tangent Formula for a given right triangle. In the parts that follow, students can go through the formulae used to calculate these ratios in further depth.

The opposing, adjacent, and hypotenuse sides of a right-angled triangle are used to define the Sine Cosine Tangent Formula in Trigonometry. These are the Sine Cosine Tangent Formula:

  • sin θ = Opposite/Hypotenuse
  • cos θ = Adjacent/Hypotenuse
  • tan θ = Opposite/Adjacent

In addition to these three trigonometric ratios, students also have the reciprocals of the Sine Cosine Tangent Formula which are denoted by the letters csc, sec, and cot, respectively. Using the example presented below, students should be able to comprehend these Sine Cosine Tangent Formula calculations:

Solved Examples

  • Example 1: Determine the triangle’s sin, cos, and tan for the specified angle.

Answer: The hypotenuse of a triangle is either its longest side or the side that faces the right angle. The perpendicular or opposing side is the side that is across from. The base or adjacent side is the side that is next to the hypotenuse.

Using the aforementioned formulae, students can now determine sin, cos, and tan:

Cos = Adjacent/Hypotenuse = 4/5 Tan = Opposite/Adjacent = 3/4 Sin = Opposite/Hypotenuse = ⅗

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