Here we will show you the basic trigonometric identities. They are to be used only for triangles that have a right angle. If the triangle is not a right triangle, none of the formulas shown below are valid. It is extremely important to keep this in mind. A triangle is a right triangle if one of the angles is equal to 90 degrees.
First make sure you examine the diagram below so you understand what the opposite and adjacent sides are.
Sine function
sin Θ =
Opposite side
Hypotenuse
sin Θ_{1} =
Opposite side
Hypotenuse

sin Θ =
Leg 2
H
sin Θ_{1} =
Leg 1
H

Cosine function
cos Θ =
Adjacent side
Hypotenuse
cos Θ_{1} =
Adjacent side
Hypotenuse

cos Θ =
Leg 1
H
cos Θ_{1} =
Leg 2
H

Tangent function
tan Θ =
Opposite side
Adjacent
tan Θ_{1} =
Opposite side
Adjacent

tan Θ =
Leg 2
Leg 1
tan Θ_{1} =
Leg 1
Leg 2

Cotangent function
cotan Θ =
Adjacent side
Opposite side
cotan Θ_{1} =
Adjacent side
Opposite side

cotan Θ =
Leg 1
Leg 2
cotan Θ_{1} =
Leg 2
Leg 1

Secant function
sec Θ =
Hypotenuse
Adjacent side
sec Θ_{1} =
Hypotenuse side
Adjacent side

sec Θ =
H
Leg 1
sec Θ_{1} =
H
Leg 2

Cosecant function
csc Θ =
Hypotenuse
Opposite side
csc Θ_{1} =
Hypotenuse
Opposite side

csc Θ =
H
Leg 2
csc Θ_{1} =
H
Leg 1

The tangent is the ratio of the sine to the cosine.
The cotangent is the inverse of the tangent.
The cosecant is the inverse of the sine
The secant is the inverse of the cosine
Dec 16, 16 01:14 PM
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