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9-12 Integrated Math 2 Unit 3

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K-5 Math 6-8 Math •9-12 Math

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Integrated Math 1 •Integrated Math 2 Integrated Math 3

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Unit 3

Glossary

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Integrated Math 2

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.

<p>A right angle, annotated.</p> — \(\arccos \left( \frac{\text{adjacent}}{\text{hypotenuse}} \right)=\theta\)

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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.

<p>A right angle, annotated.</p> — \(\arcsin \left( \frac{\text{opposite}}{\text{hypotenuse}} \right) = \theta\)

used in:

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.

<p>A right triangle, annotated.</p> — \(\arctan \left( \frac{\text{opposite}}{\text{adjacent}} \right) = \theta\)

used in:

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, \(\cos(x)=\frac{b}{c}\).

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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, \(\sin(x) = \frac{a}{c}.\)

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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, \(\tan(x) = \frac{a}{b}.\)

used in:

Trigonometric ratios relate the angles and sides of right triangles.

Three trigonometric ratios are sine, cosine, and tangent.

\(\sin(\theta)=\dfrac{\text{opposite}}{\text{hypotenuse}}\)

\(\cos(\theta)=\dfrac{\text{adjacent}}{\text{hypotenuse}}\)

\(\tan(\theta)=\dfrac{\text{opposite}}{\text{adjacent}}\)

A right triangle, annotated.

used in:

Unit 3 Resources

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