Trigonometry has its origins in ancient Egypt and possibly Babylonia. The terms “trigonon” means three angles and “metron” means measure are derived from the Greek words. Around 500-300 BC, Hellenist mathematicians used the concept of trigonometry to calculate the positions of stars and other celestial objects.
As a result, the origins of trigonometry can be traced back to practical measuring challenges involving the discovery of unknown sides and angles using right-angled triangles. Trigonometry was founded as a separate discipline of mathematics by medieval Persian mathematicians, while trigonometric (or circular) functions were developed considerably later, in the late 1500s. Trigonometric functions are used to mimic a variety of real-life events, such as changing tide levels and day duration as seasons change.
There are certain key terms to remember that is used more frequently in the concept of trigonometry.
Angles: An angle is a shape that is formed when two rays have the same endpoint. The rays forming an angle are called the arms of the angle and the point of intersection of two arms is called the vertex of the angle.
In triangle, angle is formed at the intersection of two arms or sides of a triangle; vertex is the point of intersection. Degree and radian are the two units used to measure angles.
In addition, an angle whose measure is 90° is called a right angle. It is formed when two sides are perpendicular to each other.
What is an angle bearing? How do we represent it?
Bearing is an angle that is measured in a clockwise direction starting from the north. Always bearing is represented using 3 digit numbers. Angles between 0° and 99° will always have 0 as the starting digit. For example, 54° is represented as 054°. Angles that have 3 digits will be represented as is. For example, 137° is represented as 137° itself.
How do we calculate the angle bearing?
Follow the steps shown below to measure angle bearings:
Step 1: Draw a line segment AB for which angle bearing to be measured. Refer to the image below
Step 2: As angle bearing is measured in the clockwise direction from North, draw line that represent north direction. Here, angles bearings are determined for A to B and B to A. So, the lines are drawn at A and B and name it as N. Refer to the image below.
Step 3: Measure bearing from A to B in the clockwise direction from the north direction. Similarly, measure bearing from B to A in the clockwise direction from the north direction. Refer to the image.
Step 4: Angle bearing measuring from A to B is 70°; whereas angle bearing measuring from B to A is 250°.
What is the relationship between degree and radian?
The unit of measuring angles is degree and radian.
Example 1: Convert the following degrees to radians.
Solution: To convert x° to radian, multiply x° by
Example 2: Convert the following radians to degrees.
Solution: To convert x radian to degree, multiply x by
Know more about other concepts of Trigonometry on Trigonometric Ratios and Trigonometric Identities
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