Trig Ratios
In Explore, ratios of the slopes from two triangles were compared. In mathematics, these ratios are called the tangent ratio which is one of the trigonometric ratios.
The word “trigonometric” comes from two Greek words, “trigon”, for triangle, and “meter”, for measure. The ancient Greeks discovered these ratios thousands of years ago by measuring and comparing the sides of triangles. The name of this branch of mathematics is, “trigonometry”, or “trig”.
The names given to the three ratios are the sine ratio (sin for short), the cosine ratio (cos for short), and the tangent ratio (tan for short.) These trig ratios defined for the triangle shown below.
- The sine of angle \(A\) or sin \(A=\dfrac{opp}{hyp}=\dfrac{a}{c}\)
- The cosine of angle \(A\) or cos \(A=\dfrac{adj}{hyp}=\dfrac{b}{c}\)
- The tangent of angle \(A\) or tan\(A=\dfrac{opp}{adj}=\dfrac{a}{b}\)
Find the indicated ratios for the triangle below. Leave your answers in fraction form.
- sin \(37^\circ\)=
- cos \(37^\circ\)=
- tan \(37^\circ\)=
- sin \(53^\circ\)=
- cos \(53^\circ\)=
- tan \(53^\circ\)=
