Here we will show you the basic trigonometric identities. They are 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 three right triangles in the diagram above so you understand what the opposite and adjacent sides are.
Notice that the hypotenuse is the line that is neither vertical nor horizontal.
The two triangles on top do not have any label on the triangles to identify the hypotenuse. However, the hypotenuse is the line that is slanted.
Remember that an angle is made with two sides. The side that is opposite to the angle θ is the side that is not used to create the angle. I hope this helps to identify the opposite side.
The adjacent side is one of the sides that is used to make the angle, but it is not the hypotenuse or the slanted side.
The adjacent side is going to be either the horizontal side or the vertical side.
sin θ =
Opposite side
Hypotenuse
sin θ_{1} =
Opposite side
Hypotenuse

sin θ =
Leg 2
H
sin θ_{1} =
Leg 1
H

cos θ =
Adjacent side
Hypotenuse
cos θ _{1} =
Adjacent side
Hypotenuse

cos θ =
Leg 1
H
cos θ_{1} =
Leg 2
H

tan θ =
Opposite side
Adjacent
tan θ_{1} =
Opposite side
Adjacent

tan θ =
Leg 2
Leg 1
tan θ_{1} =
Leg 1
Leg 2

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

sec θ =
Hypotenuse
Adjacent side
sec θ_{1} =
Hypotenuse side
Adjacent side

sec θ =
H
Leg 1
sec θ_{1} =
H
Leg 2

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
Nov 18, 20 01:20 PM
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