SOHCAHTOA, Sine, Cosine and Tangent : 1 - What It Means

SOHCAHTOA-----------------------------------------------------------------

This is the standard model of a right triangle displaying the adjacent, opposite and hypotenuse.

SOHCAHTOA as seen above is an acronym for remembering the formulas for sine, cosine and tangent as well as the triangle that displays the hypotenuse, opposite, adjacent as well as the right angle.

Sine -----------------------------------------------------------------

In mathematics, the sine is a trigonometric function of an angle. The sine of an acute angle is defined in the context of a right triangle: for the specified angle, it is the ratio of the length of the side that is opposite that angle to the length of the longest side of the triangle (the hypotenuse).

f = c / λ = wave speed c (m/s) / wavelength λ (m). The formula for time is: T (period) = 1 / f (frequency). λ = c / f = wave speed c (m/s) / frequency f (Hz). The unit hertz (Hz) was once called cps = cycles per second.

In mathematics, a unit circle is a circle with a radius of one. Frequently, especially in trigonometry, the unit circle is the circle of radius one centered at the origin (0, 0) in the Cartesian coordinate system in the Euclidean plane.

1. The ordinate of the endpoint of an arc of a unit circle centered at the origin of a Cartesian coordinate system, the arc being of length x and measured counterclockwise from the point (1, 0) if x is positive or clockwise if x is negative.

1. In a right triangle, the ratio of the length of the side opposite an acute angle to the length of the hypotenuse.

a. A trigonometric function that in a right-angled triangle is described as the ratio of the length of the opposite side to that of the hypotenuse of the triangle.

b. A function that in a circle centered at the origin of a Cartesian coordinate system is the ratio of the ordinate of a point on the circumference to the radius of the circle

Hypotenuse is described as the longest side of a right triangle, that is opposite to the right angle.

The law of sines is described as a law stating that the ratio of a side of a plane triangle to the sine of the opposite angle is the same for all three sides.

It is the relationship between the sides and angles of non-right (oblique) triangles . Simply, it states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all sides and angles in a given triangle.

Tangent -----------------------------------------------------------------

Tangent is described as a straight line or plane that touches a curve or curved surface at a point, but if extended does not cross it at that point for example (of a line or plane) touching, but not intersecting, a curve or curved surface.

a. A line, curve, or surface meeting another line, curve, or surface at a common point and sharing a common tangent line or tangent plane at that point.
b. Abbr. tan The trigonometric function of an acute angle in a right triangle that is the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.

The law of tangents describes the relationship between the tangent of two angles of a triangle and the lengths of the opposite sides. Unlike trigonometric functions, the law of tangents can be applied to a non-right triangle. Though not as well known as the law of sines or the law of cosines, the law of tangents is equally as powerful and can be used to find the remaining parts of a triangle if two sides and one angle or two angles and one side are known. For any triangle with angles α, β, and γ and sides a, b, and c opposite those angles respectively, the law of tangents is defined as

Cosine -----------------------------------------------------------------

1. In a right triangle, the ratio of the length of the side adjacent to an acute angle to the length of the hypotenuse.
   
2. The abscissa at the endpoint of an arc of a unit circle centered at the origin of a Cartesian coordinate system, the arc being of length x and measured counterclockwise from the point (1, 0) if x is positive or clockwise if x is negative.

The law of cosines is a law in trigonometry: the square of a side of a plane triangle equals the sum of the squares of the remaining sides minus twice the product of those sides and the cosine of the angle between them.

An example of each of these laws would be :