Trigonometric Functions

Knowledge

What are the six basic trigonometric functions?

In mathematics, trigonometric functions (also called circular functions or angle functions) are functions of angles. Trigonometric function is usually defined as the ratio of two sides of a right triangle containing this angle, or equivalent to the length of various line segments on the unit circle. We use to indicate the angle. Trigonometric functions play an important role in studying the properties of geometric shapes such as triangles and circles, and are also a basic mathematical tool for studying periodic phenomena. The six basic trigonometric functions are sine/cosine/tangent/cotangent/secant/cosecant functions.

Trigonometric functions formulas

Trigonometric function formulas seem to be many and complex, but as long as you master the essence and internal laws of trigonometric function, you will find that there is a strong relationship between the various formulas of trigonometric function.

•What is sine function?

Sine function is the ratio of the opposite side to the hypotenuse of a right triangle. The value of sine is: sinθ = ac

•What is cosine function?

Cosine is the ratio of the right angle edge adjacent to the acute angle to the hypotenuse. The value of cosine is: cosθ = bc

•What is tangent function?

Tangent function is the ratio of the side corresponding to the acute angle to another right angle side. The value of tangent is: tanθ = ab

•What is secant, cosecant and cotangent function?

Secant (sec), cosecant (csc) and cotangent (cot) are three additional functions derived from the principal functions of sine, cosecant and tangent. The reciprocal of sine, cosine, and tangent are respectively cosecant (csc), secant (sec), and cotangent (cot). The formulas for these functions are as follows:

sinθ = a b

cosθ = c a

cotθ = b a

All right, now that we have learned what is sine / cosine / tangent / secant / cosecant / cotangent function, let’s practice!

Trigonometric ratio table

The trigonometric ratio table for six trigonometric functions is:

Trigonometric functions FAQs

Question 1: Which trigonometric function is an odd function and why?

Answer: Sine is an odd function, and cosine is an even function.

Question 2: Which results from multiplying the six trigonometric functions？A.-3, B.-1, C.1, D.3

Answer: C. Use the trigonometric function formulas, since cosecant, secant and cotangent are just the reciprocals of sine, cosine and tangent, when you multiply each corresponding pair you just get 1.

Question 3: How to solve sinθ, cosθ, tanθ that are not from a right triangle?

Answer: Use the list of trigonometric identities.The triangle identities are equations that are true for all triangles

Question 4: Why do we study trigonometry?

Answer: Because trigonometric functions are widely used in life, production, aerospace, military and other fields. In real life, many periodic phenomena can be simulated by trigonometric functions, such as current, tide, etc. In addition, many maximum problems can also be converted into trigonometric functions to solve, such as weather forecast, architectural design, navigation, surveying, national defense, etc.

Question 5: Who invented trigonometry?

Answer: From the fifth century to the twelfth century, trigonometry was only a computational tool in astronomy. Around 1250, Nasir al-Din Tusi, an Arab, began to make trigonometry independent from astronomy. In 1464, On Various Triangles written by German mathematician Reg Montanus (published in 1533) was the first independent trigonometry book in Europe, in which the sine law appeared. Around 1580, The French mathematician F.Viete gave the calculation method and a complete set of formulas and memory rules for a spherical right-angled triangle, and expressed this set of formulas in algebraic form, which is Very important work.