# Trigonometrical Ratios of (360° - θ)

We will find the results of trigonometrical Ratios of (360° - θ) and (n ∙ 360° - θ).

If n is a negative integer then the trigonometrical ratios of (n ∙ 360° - θ) are equal to the trigonometrical ratios of (- θ).

Therefore,

sin (n ∙ 360° -  θ) = - sin θ;

cos (n ∙ 360° -  θ) = cos θ;

tan (n ∙ 360° -  θ= - tan θ;

csc (n ∙ 360° -  θ) = - csc θ;

sec (n ∙ 360° -  θ) = sec θ;

cot (n ∙ 360° -  θ= - cot θ.

Solved examples:

1. Find the value of sec 300°.

Solution:

sec 300° = sec (360 - 60)°

= sec 60°; since we know, sec (n ∙ 360° -  θ) = sec θ

= 2

2. Find the value of sin 270°.

Solution:

sin 270° = sin (360 - 90)°

= - sin 90°; since we know, sin (n ∙ 360° -  θ) = - sin θ

= - 1

3. Find the value of tan 330°.

Solution:

tan 330° = tan (360 - 30)°

= - tan 30°; since we know, tan (n ∙ 360° -  θ) = - tan θ

= - $$\frac{1}{√3}$$

4. Find the value of cos 315°.

Solution:

cos 315° = cos (360 - 45)°

= cos 45°; since we know, cos (n ∙ 360° -  θ) = cos θ

= $$\frac{1}{√2}$$

Trigonometric Functions

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.

## Recent Articles

1. ### Adding 1-Digit Number | Understand the Concept one Digit Number

Sep 17, 24 02:25 AM

Understand the concept of adding 1-digit number with the help of objects as well as numbers.

2. ### Counting Before, After and Between Numbers up to 10 | Number Counting

Sep 17, 24 01:47 AM

Counting before, after and between numbers up to 10 improves the child’s counting skills.

3. ### Worksheet on Three-digit Numbers | Write the Missing Numbers | Pattern

Sep 17, 24 12:10 AM

Practice the questions given in worksheet on three-digit numbers. The questions are based on writing the missing number in the correct order, patterns, 3-digit number in words, number names in figures…

4. ### Arranging Numbers | Ascending Order | Descending Order |Compare Digits

Sep 16, 24 11:24 PM

We know, while arranging numbers from the smallest number to the largest number, then the numbers are arranged in ascending order. Vice-versa while arranging numbers from the largest number to the sma…