Trigonometrical Ratios of any Angle
Math Coloring Pages
Multiplication Table
Cool Maths Games
Math Flash Cards
Online Math Quiz
Math Puzzles
Preschool Activities
Kindergarten Math
1st Grade Math
2nd Grade Math
3rd Grade Math
Custom Search
Search
We will learn how to find the trigonometrical ratios of any angle using the
following step-by-step procedure.
Step I: To find the trigonometrical ratios of angles (n ∙ 90° ± θ); where n is
an integer and θ is a positive acute angle, we will follow the below
procedure.
First we need to determine the sign of the given trigonometrical ratio. Now
to determine the sign of the given trigonometrical ratio we need to find the
quadrant in which the angle (n ∙ 90° + θ) or (n ∙ 90° - θ) lies.
math sheets
sin cos tan
cot changes to
acute angle
cosine ratio
Now, using the rule “All, sin, tan, cos” we will find the sign of the given
trigonometrical ratio.Therefore,
(i) All trigonometrical ratios are positive if the given angle (n ∙ 90° + θ) or
(n .90° + θ) lies in the I quadrant (first quadrant);
4th Grade Math
5th Grade Math
6th Grade Math
7th Grade Math
8th Grade Math
9th Grade Math
10th Grade Math
11 & 12 Grade Math
Matrix
Probability
Algebra 1
Concepts of Sets
Logarithms
Boolean Algebra
Statistics
(ii) Only sin and csc ratios is positive if the given angle (n ∙ 90° + θ) or (n ∙
90° - θ) lies in the II quadrant (second quadrant);
(iii) Only tan and cot ratios is positive if the given angle (n ∙ 90° + θ) or (n ∙
90° - θ) lies in the III quadrant (third quadrant);
(iv) Only cos and sec ratios is positive if the given angle (n ∙ 90° + θ) or (n
∙ 90° - θ) lies in the IV quadrant (fourth quadrant).
Binary System
Math Dictionary
Conversion Chart
Homework Sheets
Step II: Now determine whether n is an even or odd integer.
(i) If n is an even integer the form of the given trigonometrical ratio will
remain the same i.e.,
Math Problem Ans
Free Math Answers
sin (n ∙ 90° + θ) = sin θ
csc (n ∙ 90° + θ) = csc θ
Printable Math Sheet
sin (n ∙ 90° - θ) = - sin θ;
csc (n ∙ 90° - θ) = - csc θ;
cos (n ∙ 90° + θ) = cos θ;
sec (n ∙ 90° + θ) = sec θ;
cos (n ∙ 90° - θ) = - cos θ;
sec (n ∙ 90° - θ) = - sec θ;
tan (n ∙ 90° + θ) = tan θ;
cot (n ∙ 90° + θ) = cot θ;
Funny Math Answers
Employment Test
https://www.math-only-math.com/trigonometrical-ratios-of-any-angle.html
1/4
Trigonometrical Ratios of any Angle | “All, sin, tan, cos” Rule | Examples
4/28/2020
Link Partners
tan (n ∙ 90° - θ) = - tan θ.
cot (n ∙ 90° - θ) = - cot θ.
About Us
Contact Us
Site Map
[?]Subscribe To This Site
E-mail Address
(ii) If n is an odd integer then the form of the given trigonometrical ratio is
altered i.e.,
sin changes to cos;
csc changes to sec;
i.e., sin (n ∙ 90° + θ) = cos θ
i.e., csc (n ∙ 90° + θ) = sec θ
or, sin (n ∙ 90° - θ) = - cos θ
or, csc (n ∙ 90° - θ) = - sec θ
cos changes to sin;
sec changes to csc;
i.e., cos (n ∙ 90° + θ) = sin θ
i.e., sec (n ∙ 90° + θ) = csc θ
or, cos (n ∙ 90° - θ) = - sin θ
or, sec (n ∙ 90° - θ) = - csc θ
tan changes to cot;
cot changes to tan;
i.e., tan (n ∙ 90° + θ) = cot θ
i.e., cot (n ∙ 90° + θ) = tan θ
or, tan (n ∙ 90° - θ) = - cot θ
or, cot (n ∙ 90° - θ) = - tan θ
First Name
Then
Subscribe
Don't worry — your e-mail
address is totally secure.
I promise to use it only to
send you Math Only Math.
● Trigonometric Functions
B asic Trigonometric Ratios and Their
Names Restrictions of Trigonometrical
Ratios
R eciprocal Relations of Trigonometric Ratios
Quotient Relations of Trigonometric Ratios
L imit of Trigonometric
Ratios T rigonometrical
Identity
P roblems on Trigonometric
Identities E limination of
Trigonometric Ratios
E liminate Theta between the
equations Problems on Eliminate
Theta
Trig Ratio Problems
P roving Trigonometric
Ratios T rig Ratios Proving
Problems
Verify Trigonometric
Identities T rigonometrical
Ratios of 0°
T rigonometrical Ratios of
30° T rigonometrical Ratios of
45° T rigonometrical Ratios of
60° T rigonometrical Ratios of
90° T rigonometrical Ratios
Table
P roblems on Trigonometric Ratio of Standard
Angle T rigonometrical Ratios of Complementary
Angles
Rules of Trigonometric Signs
S igns of Trigonometrical
Ratios All Sin Tan Cos Rule
https://www.math-only-math.com/trigonometrical-ratios-of-any-angle.html
2/4
Trigonometrical Ratios of (- θ)
T rigonometrical Ratios of (90° +
θ) T rigonometrical Ratios of (90° θ)
T rigonometrical Ratios of (180° +
θ) T rigonometrical Ratios of (180° θ)
T rigonometrical Ratios of (270° + θ)
Trigonometrical Ratios of (270° - θ)
https://www.math-only-math.com/trigonometrical-ratios-of-any-angle.html
3/4