Loading [MathJax]/jax/output/HTML-CSS/jax.js

Signs of Trigonometrical Ratios

Here we will discuss about the signs of trigonometrical ratios.

Let a rotating line OA rotates about O in the anti-clockwise direction or clockwise direction. Suppose starting from the rotating line OA as the initial position OX take ∠XOA = θ. Take a point B on OA and a line is drawn which is ¯BC perpendicular to OA (or OX). Therefore, by the definition of trigonometrical ratios of the angle θ of the right-angled triangle OBC are:

sin θ = CB/OB = opposite side/hypotenuse;

cos θ = OC/OB = adjacent side/hypotenuse;

tan θ = CB/OC = opposite side/adjacent side;

csc θ = OB/CB = hypotenuse/opposite side

sec θ = OB/OC = hypotenuse/adjacent side;

cot θ = OC/CB = adjacent side/opposite side

Signs of Trigonometrical Ratios

According to the value of θ the final arm OA would be in the first quadrant or second quadrant or third quadrant or fourth quadrant:

Case 1: When the final arm OA lies in the first quadrant

θ Lies in the First Quadrant

According to the trigonometric rules, we get

OC is positive,

CB is positive and

OB is positive.

Therefore, according to the definitions of trigonometrical ratios the values of all trigonometrical ratios i.e. sin θ, cos θ, tan θ, csc θ, sec θ and cot θ are positive.


Case 2: When the final arm OA lies in the second quadrant.

θ Lies in the Second Quadrant

According to the trigonometric rules, we get

OC is negative,

CB is positive and

OB is positive.

Therefore, according to the definitions of trigonometrical ratios the values of sin θ and csc θ are positive and the other trigonometrical ratios i.e. cos θ, tan θ, sec θ and cot θ are negative. 


Case 3:  When the final arm OA lies in the third quadrant. 

θ Lies in the Third Quadrant

According to the trigonometric rules, we get

OC is negative;

CB is negative and

OB is positive.

Therefore, according to the definitions of trigonometrical ratios the values of tan θ and cot Ѳ are positive and the other trigonometrical ratios i.e. sin θ, cos θ, sec θ and csc θ are negative.


Case 4: When the final arm OA lies in the fourth quadrant.

θ Lies in the Fourth Quadrant

According to the trigonometric rules, we get

OC is positive;

CB is negative and

OB is positive.

Therefore, according to the definitions of trigonometrical ratios the values of cos θ and sec θ are positive and the other trigonometrical ratios i.e. sin θ, tan θ, csc θ and cot θ are negative.

 Trigonometric Functions





11 and 12 Grade Math

From Signs of Trigonometrical Ratios to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.




Share this page: What’s this?

Recent Articles

  1. Worksheet on 8 Times Table | Printable Multiplication Table | Video

    Mar 18, 25 03:30 PM

    worksheet on multiplication of 8 times table
    Worksheet on 8 times table can be printed out. Homeschoolers can also use these multiplication table sheets to practice at home.

    Read More

  2. Worksheet on Roman Numerals |Roman Numerals|Symbols for Roman Numerals

    Mar 18, 25 02:47 PM

    Roman Numbers Table
    Practice the worksheet on roman numerals or numbers. This sheet will encourage the students to practice about the symbols for roman numerals and their values. Write the number for the following: (a) V…

    Read More

  3. Conversion of Roman Numeration | Roman Numerals |Hindu Arabic Numerals

    Mar 18, 25 02:12 PM

    We will learn the conversion of Roman numeration. First we will learn how to convert numbers in roman numerals. 1. Convert 579 in roman numerals.

    Read More

  4. Rules of Roman Numeration |Roman Number System|Roman Numeration System

    Mar 18, 25 09:41 AM

    Rules of Roman Numerals
    We will learn about Roman Numeration and its rules. We know that there are seven basic Roman Numerals. They are I, V, X, L, C, D and M. These numerals stand for the number 1, 5, 10, 50, 100, 500

    Read More

  5. Divisible by 2 | Test of Divisibility by 2 |Rules of Divisibility by 2

    Mar 17, 25 04:04 PM

    Divisible by 2
    A number is divisible by 2 if the digit at unit place is either 0 or multiple of 2. So a number is divisible by 2 if digit at its units place is 0, 2, 4, 6 or 8.

    Read More