Trigonometric ratios

Choose sides relative to a reference angle and find sine, cosine, and tangent.

Meaning

For an acute angle of a right triangle, sine is opposite/hypotenuse, cosine adjacent/hypotenuse, and tangent opposite/adjacent. Right triangles sharing that acute angle are similar and have equal ratios.

Example

With hypotenuse 10, opposite side 6, and adjacent side 8, the angle's sine is cosine and tangent Opposite and adjacent depend on the chosen angle. The hypotenuse is always opposite the right angle.

Practice for this concept

Scope and references

Topics

Sine, cosine, tangent, right-triangle side ratios, special-angle ratios

Learning goal

Choose sides relative to a reference angle and find sine, cosine, and tangent.

Helpful background

Explore side positions relative to an angle and ratios in similar triangles.