(11) MTH1.2: The Primary Trigonometric Ratios

Trigonometry

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

5 Main Properties in a Right Triangle

(1) Has one 90° angle, (2) The hypotenuse is the side across from the 90° angle, (3) The reference angle is either of the other two angles—never the 90° angle, (4) The opposite side is the side across from the reference angle, and (5) 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 and angles in a right triangle.

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

(1) Use the [INV] or [Shift] key, (2) Followed by sin⁻¹, cos⁻¹, or tan⁻¹, (3) Then, followed by the ratio, and (4) Calculate and round the answer to the nearest one.

5 Steps for Calculating an Unknown Side Using Trig Ratios

(1) Label the sides and angles, (2) Write the Trig Ratios formula for the side you are finding, (3) Substitute the values, (4) Isolate for the variable by cross-multiplying, and (5) Write a final statement.

6 Steps for Calculating an Unknown Angle Using Trig Ratios

(1) Label the sides and angles, (2) Write the Trig Ratios formula for the angle you are finding, (3) Substitute the values, (4) Simplify, (5) Isolate for the angle using inverse trig, and (6) Write a final statement.