Mastering Trigonometry: Functions, Rules And Theorems For Calculating Triangles

Trigonometry

The measurement of triangles

1. What is trigonometry?
Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It is used to calculate the angles and lengths of sides of triangles in various applications like astronomy, physics, engineering, and surveying.

2. What are the three main trigonometric functions?
The three main trigonometric functions are sine, cosine, and tangent. They are abbreviated as sin, cos, and tan, respectively.

3. What is the Pythagorean theorem?
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In equation form, it can be written as a² + b² = c², where a and b are the lengths of the two legs of the triangle, and c is the length of the hypotenuse.

4. What is the unit circle?
The unit circle is a circle with a radius of one unit. It is centered at the origin (0,0) in the coordinate plane. The unit circle is used in trigonometry to define the trigonometric functions of any angle in the standard position.

5. What is the difference between radians and degrees?
Radians and degrees are two units of measurement for angles. Degrees are based on dividing a circle into 360 equal parts, while radians are based on dividing a circle into 2π (approximately 6.28) equal parts. Radians are commonly used in calculus and trigonometry, while degrees are used more often in everyday applications.

6. What is the sine rule?
The sine rule relates the side lengths and angles of a triangle. It states that in any triangle, the ratio of the length of a side to the sine of the angle opposite that side is the same for all three sides. The equation can be written as a/sin A = b/sin B = c/sin C, where a, b, and c are the lengths of the sides, and A, B, and C are the angles opposite those sides.

7. What is the cosine rule?
The cosine rule, also known as the law of cosines, is used to find the length of a side or the size of an angle in a triangle given the lengths of the other sides and angles. It states that in any triangle, the square of a side is equal to the sum of the squares of the other two sides, minus twice the product of those sides and the cosine of the angle between them. The equation can be written as c² = a² + b² – 2ab cos C, where c is the length of the side opposite the angle C, and a and b are the lengths of the other two sides.

8. What is the tangent rule?
The tangent rule relates the sides and angles in a right-angled triangle. It states that in a right-angled triangle, the ratio of the length of the side opposite an acute angle to the length of the adjacent side is equal to the tangent of that angle. The equation can be written as tan A = opposite/adjacent, tan B = opposite/adjacent, or tan C = opposite/adjacent, depending on which angle is being considered.

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