Table of Contents
Introduction to Trigonometry
Trigonometry is the study of relationships between the sides and angles of triangles. It is a branch of mathematics that deals with the measurement of angles and the calculation of lengths and areas in triangles.
The word trigonometry is derived from the Greek words trigonon (triangle) and metron (measurement). Trigonometry is often used in physics, engineering, and surveying.
Applications of Trigonometry:
There are a number of applications of trigonometry in the real world. Some of these applications include surveying, navigation, construction, and astronomy.
Surveying: Trigonometry is used in surveying to calculate distances and angles. This is done by using trigonometric functions to calculate the height of a point above or below a reference point, the length of a line, or the angle between two lines.
Navigation: Trigonometry is used in navigation to calculate the distances and angles between two points. This is done by using trigonometric functions to calculate the height of a point above or below a reference point, the length of a line, or the angle between two lines.
Construction: Trigonometry is used in construction to calculate the angles and distances between two points. This is done by using trigonometric functions to calculate the height of a point above or below a reference point, the length of a line, or the angle between two lines.
Astronomy: Trigonometry is used in astronomy to calculate the distances and angles between two points. This is done by using trigonometric functions to calculate the height of a point above or below a reference point, the length of a line, or the angle between two lines.
Trigonometric Angles in Radians
A radian is a unit of angular measurement equal to the angle subtended at the center of a circle by an arc of length equal to the radius of the circle. Radians are abbreviated as rad.
There are 2π radians in a full circle.
A radian is also equal to the angle subtended by an arc of length 1 at the center of the circle. Therefore, there are π radians in a half-circle.
A radian is also equal to the angle subtended by an arc of length r at the center of the circle. Therefore, there are r/2 radians in a quarter-circle.
The following is a list of common angles in radians:
0 radians (or 0°)
= 360°
1 radian
= 57.3°
2 radians
= 114.6°
3 radians
= 171.9°
4 radians
= 228.2°
5 radians
= 285.5°
6 radians
= 342.8°
7 radians
= 400.1°
8 radians
= 457.3°
9 radians
= 514.6°
10 radians
= 571.9°
11 radians
= 629.2°
12 radians
= 686.5°
13 radians
= 743.8
Trigonometric Angles in Degrees
There are 360 degrees in a circle.
Angles can be measured in degrees, radians, or gradians.
One degree is 1/360th of a circle.
One radian is the angle formed by the length of the radius of a circle divided by the length of the circumference of the circle.
There are 400 gradians in a circle.
How to find the Value of Cos 60?
The value of cos 60 is 0.5.
How to improve Scores in Trigonometry
There is no definitive answer to this question since everyone learns in different ways and some students may be naturally better at trigonometry than others. However, some general tips that may help improve scores in trigonometry include:
-Studying regularly and keeping up with homework assignments.
-Attending class regularly and taking notes.
-Participating in class discussions.
-Asking questions in class if something is not clear.
-Working through practice problems.
-Using a tutor if needed.
FAQs
Q: What is trigonometry?
A: Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles.
Q: What are sine, cosine, and tangent?
A: Sine, cosine, and tangent are the three primary trigonometric functions that relate the angles of a triangle to the lengths of its sides. The sine function relates the opposite side to the hypotenuse, the cosine function relates the adjacent side to the hypotenuse, and the tangent function relates the opposite side to the adjacent side.
Q: What is the Pythagorean theorem?
A: The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Q: What is an angle?
A: An angle is the measure of the amount of rotation between two intersecting lines. It is usually measured in degrees or radians.
Q: What is a radian?
A: A radian is a unit of measurement for angles, where one radian is the angle formed when the radius of a circle is wrapped around the circumference of the circle.
Q: What is the unit circle?
A: The unit circle is a circle with a radius of one unit that is centered at the origin of a coordinate plane. It is used in trigonometry to relate the values of the trigonometric functions to the angles on the circle.
Q: What is the inverse trigonometric function?
A: The inverse trigonometric functions are used to find the angle that corresponds to a given value of a trigonometric function. The inverse functions include arcsine, arccosine, and arctangent.
Q: What is the law of sines?
A: The law of sines is a relationship that exists between the sides and angles of a non-right triangle. It states that the ratio of the length of a side to the sine of the opposite angle is constant for all sides and angles in the triangle.
Q: What is the law of cosines?
A: The law of cosines is a relationship that exists between the sides and angles of a non-right triangle. It relates the length of one side to the other two sides and the cosine of the angle opposite the first side.
