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Definition from a right triangle

A right triangle has an angle of 90 ° ( π / 2 radians), here C, and angles A and B are variable. Trigonometric functions define the relationship between side lengths and internal angles of a triangle. Right angle In defining the trigonometric functions for angle A, we assign one of the angles in a right triangle to A. Each side of the triangle is named as:

The hypotenuse (hypotenuse) is the side opposite the right angle. Or the longest side of a right triangle, here is h.
The opposite (opposite side) is the side opposite the angle we are interested in is a.
The contiguous (adjacent side) is the side adjacent to the angle we are interested in this angle and b.

Will get

1). The sine of the angle is the ratio of the length of the opposite side. To the length of the hypotenuse, here is

sin ( A ) = skip / scene = a / h

2). The cosine of an angle is the ratio of the adjacent side lengths. To the length of the hypotenuse, here is

cos ( A ) = align / right = b / h

3). The tangent of an angle is the ratio of the length of the opposite side. Per adjacent side length, here is

tan ( A ) = cross / align = a / b

4). The cosecant csc ( A ) is the multiplicative inverse function of sin ( A ), that is, the ratio of the length of the hypotenuse. Per side length

csc ( A ) = scene / skip = h / a

5). The secant sec ( A ) is the multiplicative inverse function of cos ( A ), that is, the ratio of the length of the hypotenuse. Per side length

sec ( A ) = scene / align = h / b

6). The cotangent cot ( A ) is the multiplication inverse function of tan ( A ), that is, the ratio of the adjacent side lengths. Per side length

cot ( A ) = align / skip = b / a

How to remember

A simple way to remember is to remember that cross-aligned, aligned, cross-aligned.

  • Scene … sin sin = side opposite / opposite corner of the scene.
  • Intimate scene … the cos = on the right / at the opposite corner of the scene.
  • Across the alignment … tan = opposite side / aligned side

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