Trigonometric Ratios


a right triangle

Trigonometrical ratios

If there is a right angled triangle with base (b), hypotenuse (h) and perpendicular (p).  α is the angle between the base and the hypotenuse then

sine

The ratio of perpendicular (p) to hypotenuse (h) of the triangle is called the sine of the angle α.
sin α = p/h.

cos

The ratio of base (b) to hypotenuse (h) of the triangle is called the cosine of the angle α.
cos α = b/h.

tan

The ratio of perpendicular (p) to base (b) of the triangle is called the tangent of the angle α.
tan α = p/b.

On dividing numerator and denominator by h we get.
tan α = (p/h)/(b/h).
As p/h = sin α and b/h = cos α.
So, we can write tan α as sin α/cos α
tan α = sin α/cos α

cot

The ratio of base (b) to perpendicular (p) of the triangle is called the cotangent of the angle α.
cot α = b/p.

On dividing numerator and denominator by h we get.
cot α = (b/h)/(p/h).
As p/h = sin α and b/h = cos α.
So, we can write cot α as cos α/sin α
cot α = cos α/sin α

sec

The ratio of hypotenuse (h) to base (b) of the triangle is called the secant of the angle α.
sec α = h/b.

as cos α = b/h
So, sec α = 1/cos α

cosec

The ratio of hypotenuse (h) to perpendicular (p) of the triangle is called the cosecant of the angle α.
cosec α = h/p.

as sin α = p/h
So, cosec α = 1/sin α

Ratios


ratios
denominator\numerator p h b
p 1 cosec cot
h sin 1 cos
b tan sec 1

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