# Trigonometrical Ratios of some Particular Angles

Trigonometrical ratios of some particular angles i.e., 120°, -135°, 150° and 180° are given below.

1. sin 120° = sin (1 × 90° + 30°) = cos 30° = $$\frac{√3}{2}$$;

cos 120° = cos (1 × 90° + 30°) = - sin 30° = - $$\frac{1}{2}$$;

tan 120° = tan (1 × 90° + 30°) = - cot 30° = - √3;

csc 120° = csc (1 × 90° + 30°) = sec 30° = $$\frac{2}{√3}$$;

sec 120° = sec (1 × 90° + 30°) = - csc 30° = - 2;

tan 120° = tan (1 × 90° + 30°) = - cot 30° = - √3;

cot 120° = cot (1 × 90° + 30°) = - tan 30° = - $$\frac{1}{√3}$$.

2. sin (- 135°)= - sin 135°= - sin (1 × 90°+ 45°) = - cos 45° = - $$\frac{1}{√2}$$;

cos (- 135°)= cos 135°= cos (1 × 90°+ 45°) = - sin 45°= - $$\frac{1}{√2}$$;

tan (- 135°) = - tan 135° = - tan ( 1 × 90° + 45°) = - (- cot 45°) = 1;

csc (- 135°)= - csc 135°= - csc (1 × 90°+ 45°)= - sec 45° = - √2;

sec (- 135°)= sec 135°= sec (1 × 90°+ 45°)= - csc 45°= - √2;

cot (- 135°) = - cot 135° = - cot ( 1 × 90° + 45°) = - (-tan 45°) = 1.

3. sin 150° = sin (2 × 90° - 30°) = sin 30° = 1/2;

cos 150° = cos (2 × 90° - 30°) = cos 30° = - $$\frac{√3}{2}$$;

tan 150° tan (2 × 90° - 30°) = - tan 30° = - $$\frac{1}{√3}$$;

csc 150° = csc (2 × 90° - 30°) = csc 30° = 2;

sec 150° = sec (2 × 90° - 30°) = sec 30° = - $$\frac{2}{√3}$$;

cot 150° = cot (2 × 90° - 30°) = - cot 300 = - √3.

4. sin 180° = sin (2 × 90° - 0°) = sin 0° = 0;

cos 180° = cos (2 × 90° - 0°) = - cos 0° = - 1;

tan 180° = tan (2 × 90° + 0°) = tan 0° = 0;

csc 180° = csc (2 × 90° - 0°) = csc 0° = Undefined;

sec 180° = sec (2 × 90° - 0°) = - sec 0° = - 1;

cot 180° = cot (2 × 90° + 0°) = cot 0° = Undefined.

5. sin 270° = sin (3 × 90° + 0°) = - cos 0° = - 1;

cos 270° = cos (3 × 90° + 0°) = sin 0° = 0;

tan 270° = tan (3 × 90° + 0°) = - cot 0° = Undefined;

csc 270° = csc (3 × 90° + 0°) = - sec 0° = - 1;

sec 270° = sec (3 × 90° + 0°) = csc 0° = Undefined;

cot 270° = cot (3 × 90° + 0°) = - tan 0° = 0.

These trigonometrical ratios of some particular angles (120°, -135°, 150° and 180°) are required to solve various problems.

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. ### Expanded form of Decimal Fractions |How to Write a Decimal in Expanded

Jul 22, 24 03:27 PM

Decimal numbers can be expressed in expanded form using the place-value chart. In expanded form of decimal fractions we will learn how to read and write the decimal numbers. Note: When a decimal is mi…

2. ### Worksheet on Decimal Numbers | Decimals Number Concepts | Answers

Jul 22, 24 02:41 PM

Practice different types of math questions given in the worksheet on decimal numbers, these math problems will help the students to review decimals number concepts.

3. ### Decimal Place Value Chart |Tenths Place |Hundredths Place |Thousandths

Jul 21, 24 02:14 PM

Decimal place value chart are discussed here: The first place after the decimal is got by dividing the number by 10; it is called the tenths place.

4. ### Thousandths Place in Decimals | Decimal Place Value | Decimal Numbers

Jul 20, 24 03:45 PM

When we write a decimal number with three places, we are representing the thousandths place. Each part in the given figure represents one-thousandth of the whole. It is written as 1/1000. In the decim…