Basic Trigonometry

What is Trigonometry (Trigonometri)?

Trigonometry is a branch of mathematics that studies relationships between the sides and angles of triangles.Trigonometry comes from the two roots, trigonon (or “triangle”) and metria (or “measure”). The study of trigonometry is thus the study of measurements of triangles.

Hypotenuse, Opposite and Adjacent (Hipotenus, Sisi Bertenangan, Sisi Bersebelahan)

The hypotenuse (hipotenus) of a right triangle is always the side opposite the right angle. It is the longest side in a right triangle.

The other two sides are called the opposite and adjacent sides. These sides are labelled in relation to an angle.

The opposite side (sisi bertentangan) is across from a given angle.

The adjacent side (sisi bersebelahan) is the non-hypotenuse side that is next to a given angle.

Trigonometric Ratios in Right Triangles (Segi Tiga Kanan)The ratios of the sides of a right triangle are called trigonometric ratios. Three common trigonometric ratios are the sine (sin), cosine (cos), and tangent (tan). These are defined for acute angle A below:

In these definitions, the terms opposite, adjacent, and hypotenuse refer to the lengths of the sides.

SOH-CAH-TOA: an easy way to remember trigonometric ratios

The word soh-cah-toa helps us remember the definitions of sine, cosine, and tangent. Here's how it works:

For example, if we want to recall the definition of sine, we refer SOH, since sine starts with the letter S. The O and the H help us to remember that sine is opposite over hypotenuse!

Complementary Angles (Sudut Pelengkap)

We want to prove that the sine of an angle equals the cosine of its complement.

Let's start with a right triangle. Notice how the acute angles are complementary, sum to 90°.

Now here's the cool part. See how the sine of one acute angle.

describes the exact same ratio as the cosine of the other acute angle?

Incredible! Both functions, sin (θ) = cos (90° - θ), give the exact same side ratio in a right triangle.

Reciprocal Trigonometric Ratios

The cosecant (csc)

The cosecant is the reciprocal of the sine. It is the ratio of the hypotenuse to the side opposite a given angle in a right triangle.

The secant (sec)

The secant is the reciprocal of the cosine. It is the ratio of the hypotenuse to the side adjacent to a given angle in a right triangle.

The cotangent (cot)

The cotangent is the reciprocal of the tangent. It is the ratio of the adjacent side to the opposite side in a right triangle.

How do people remember this stuff?

For most people, it's easiest to remember these new ratios by relating them to their reciprocals. The table below summarizes these relationships.

Basic Angles:

Negative Angles (Sudut Negatif):

Complementary Angles:

Special Angles (Sudut Istimewa):

A simple way to memorize the special angle

• Write the special angles (0,30,45,60,90).
• Write the integers 0 thru 4.
• Squareroot each number.
• Divide each number by 2. This gives you sine of theta.
• Write the numbers in reverse order. This gives you cosine of theta.
• Divide the previous two rows (sine over cosine). This gives you tangent theta.

Source: https://www.youtube.com/watch?v=PUB0TaZ7bhA
Test yourself !