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Trigonometric Ratios (The Basics)

Common Core Standard: G.SRT. 6 High School Geometry
Other Trigonometric Ratios

There are 3 co-functions:

Secant is the reciprocal of cosine.
Cosecant is the reciprocal of sine.
Cotangent is the reciprocal of tangent.

Secant = Hypotenuse/Adjacent  = 1/Cosine

Cosecant = Hypotenuse/Opposite = 1/Sine

Cotangent = Adjacent/Opposite = 1/Tangent



Transcript: Trigonometric Ratios (The Basics)

​Trigonometric ratios (The Basics) The trigonometric ratios are special measurements of a right triangle. In fact, trigon is Greek for triangle, and metric is Greek for measurement. Put these together and trigonometric means triangle measurement.  

Triangles have six parts, three angles, and three sides. 
Using trigonometric ratios enables you can to find any measure of a triangle if you know just two of the parts.

  • The hypotenuse is always opposite the right angle.
  • The adjacent side is the leg closest to the reference angle. ( Angle A )
  • ​The opposite side is the leg opposite the reference angle ( Angle A )












Trigonometric Ratios Chart

Hi welcome to MooMooMath. Today we are going to talk about some basic trig functions. There are three basic trig functions that we use in Geometry. They are sine, cosine, and tangent, and you will see those keys on the calculator. For these three functions you will use a right triangle. So let’s draw a right triangle, and we are going to lay out the basics of  the three ratios. We will look from the perspective of the angle in the bottom left corner labeled A, which an acute angle. From angle A, we have to set up some ratios,based on the sides that we will label. The side opposite angle A is called the opposite side. The side opposite the right angle is the hypotenuse, and the third side is the adjacent side. So the three sides are the opposite, hypotenuse, and the adjacent leg. Using these three sides we will set up the three trigonometric ratios. The first ratio is the sin of the angle A, and the sin of angle A will equal the opposite side over the adjacent or O over A. The cosine of angle A is equal to the adjacent over the hypotenuse,so it will be abbreviated A over H. The third ratio is tangent of A, which is equal to opposite over adjacent or O over A. We have a cheat sheet. We have sine which is opposite over hypotenuse, cosine is adjacent over hypotenuse, and tangent is opposite over adjacent. You can remember the trig ratios using, SOH, CAH, TOA. S = Sine = Opposite over Hypotenuse,C= Cosine = Adjacent over hypotenuse, and T = Tangent = Opposite over Adjacent.  Hope this video was helpful. 



 Math students use SOH CAH TOA in order to help them remember the trig functions.
trigonometric ratios

If you have the following information:

A right angle

Length of opposite leg

Length of the hypotenuse

Use Sine

 

Opposite

Hypotenuse

Remember using

 

SOH

A right angle

Length of adjacent leg

Length of the hypotenuse

Use Cosine

 

Adjacent

Hypotenuse

CAH

A right angle

Length of opposite leg

Length of the adjacent

Use Tangent

 

Opposite

Adjacent

TOA

 

A
C
B
opposite over hypotenuse right triangle/trigonometric ratios(the basics)
right triangle adjacent opposite highlighted
adjacent hypotenuse highlighted  right triangle
Related sites for Trig Ratios

Basic Trigonometry: Sin, Cos, Tan (mathbff)    This video shows how to find sin, cos, and tan using SohCahToa

Trig Ratios Information,facts, and fun activities covering trig ratios