(11) MTH1.2: The Primary Trigonometric Ratios

Trigonometry

A branch of mathematics that studies the properties of triangles, and trigonometric functions and their applications.

4 Main Properties in a Right Triangle

(1) The hypotenuse is the side across from the 90° angle, (2) The reference angle is either of the other two angles—never the 90° angle, (3) The opposite side is the side across from the reference angle, and (4) The adjacent side is the side between the reference angle and the 90° angle.

Trigonometric Ratios

Ratios comparing two sides of a right triangle, used to find unknown sides or angles.

3 Primary Trigonometric Ratios

Sine (sin), Cosine (cos), and Tangent (tan): Soh-Cah-Toa.

Sine (sin)

A trigonometric ratio that compares the opposite side to the hypotenuse in a right triangle: sin(angle) = opposite/hypotenuse.

Cosine (cos)

A trigonometric ratio that compares the adjacent side to the hypotenuse in a right triangle: cos(angle) = adjacent/hypotenuse.

Tangent (tan)

A trigonometric ratio that compares the opposite side to the adjacent in a right triangle: tan(angle) = opposite/adjacent.

θ (“theta”)

The Greek symbol used to represent angles.

4 Steps to Finding an Angle Using Inverse Trig From Side Ratios

5 Steps for Calculating an Unknown Side Using Trig Ratios

6 Steps for Calculating an Unknown Side Using Trig Ratios