Unit 4
Glossary
Geometry
Arccosine is a relationship used to find an acute angle measure in a right triangle when two side lengths are known.
The arccosine of a number between 0 and 1 is the measure of an acute angle whose cosine is that number.
\(\arccos \left( \frac{\text{adjacent}}{\text{hypotenuse}} \right)=\theta\)
Arcsine is a relationship used to find an acute angle measure in a right triangle when two side lengths are known.
The arcsine of a number between 0 and 1 is the measure of an acute angle whose sine is that number.
\(\arcsin \left( \frac{\text{opposite}}{\text{hypotenuse}} \right) = \theta\)
Arctangent is a relationship used to find an acute angle measure in a right triangle when two side lengths are known.
The arctangent of a positive number is the measure of an acute angle whose tangent is that number.
\(\arctan \left( \frac{\text{opposite}}{\text{adjacent}} \right) = \theta\)
The cosine of an acute angle in a right triangle is the ratio (quotient) of the length of the adjacent leg to the length of the hypotenuse.
In this diagram, \(\cos(x)=\frac{b}{c}\).
The sine of an acute angle in a right triangle is the ratio (quotient) of the length of the opposite leg to the length of the hypotenuse.
In this diagram, \(\sin(x) = \frac{a}{c}.\)
The tangent of an acute angle in a right triangle is the ratio (quotient) of the length of the opposite leg to the length of the adjacent leg.
In this diagram, \(\tan(x) = \frac{a}{b}.\)
Trigonometric ratios relate the angles and sides of right triangles.
Three trigonometric ratios are sine, cosine, and tangent.
\(\sin(\theta)=\dfrac{\text{opposite}}{\text{hypotenuse}}\)
\(\cos(\theta)=\dfrac{\text{adjacent}}{\text{hypotenuse}}\)
\(\tan(\theta)=\dfrac{\text{opposite}}{\text{adjacent}}\)