Cosec 240.
Trigonometry is a discipline of mathematics that studies the relationships between the lengths of the sides and angles of a correctangled triangle. Trigonometric functions, also known every bit goniometric functions, angle functions, or circular functions, are functions that establish the relationship between an angle to the ratio of two of the sides of a rightangled triangle. The vi primary trigonometric functions are sine, cosine, tangent, cotangent, secant, or cosecant.
Angles defined by the ratios of trigonometric functions are known as trigonometry angles. Trigonometric angles represent trigonometric functions. The value of the angle can be anywhere between 0360°.
As given in the above figure in a rightangled triangle:

Hypotenuse:
The side opposite to the right angle is the hypotenuse, It is the longest side in a correctangled triangle and opposite to the 90° bending. 
Base of operations:
The side on which angle C lies is known every bit the base. 
Perpendicular:
It is the side contrary to angle C in consideration.
Daftar Isi:
Trigonometric Functions
Trigonometry has 6 basic trigonometric functions, they are sine, cosine, tangent, cosecant, secant, and cotangent. Now let’s look into the trigonometric functions. The six trigonometric functions are as follows:

sine:
It is defined every bit the ratio of perpendicular and hypotenuse and Information technology is represented as sin θ 
cosine:
It is defined as the ratio of base and hypotenuse and it is represented as cos θ 
tangent:
Information technology is divers equally the ratio of sine and cosine of an angle. Thus the definition of tangent comes out to be the ratio of perpendicular and base and is represented as tan θ 
cosecant:
It is the reciprocal of sin θ and is represented as cosec θ. 
secant:
It is the reciprocal of cos θ and is represented equally sec θ. 
cotangent:
It is the reciprocal of tan θ and is represented as cot θ.
According to above given paradigm, Trigonometric Ratios are

Sin θ
= Perpendicular / Hypotenuse = AB/AC 
Cosine θ
= Base / Hypotenuse = BC / AC 
Tangent θ
= Perpendicular / Base of operations = AB / BC 
Cosecant θ
= Hypotenuse / Perpendicular = Air conditioning/AB 
Secant θ
= Hypotenuse / Base = AC/BC 
Cotangent θ
= Base / Perpendicular = BC/AB
Reciprocal Identities
Sin θ = 1/ Cosec θ Or Cosec θ = 1/ Sin θ
Cos θ = 1/ Sec θ Or Sec θ = 1 / Cos θ
Cot θ = ane / Tan θ Or Tan θ = 1 / Cot θ
Cot θ = Cos θ / Sin θ Or Tan θ = Sin θ / Cos θ
Tan θ.Cot θ = 1
Values of Trigonometric Ratios
0°  thirty°  45°  60°  90°  

Sin θ  1/two  1/√two  √3/2  1  
Cos θ  1  √3/2  1/√2  ane/2  
Tan θ  1√3  1  √3  Not Defined  
Cosec θ  Non Defined  2  √2  2/√iii  1 
Sec θ  1  2/√3  √2  2  Not Defined 
Cot θ  Non Defined  √3  1  ane/√iii 
Trigonometric Identities of Complementary and Supplementary Angles

Complementary Angles:
Pair of angles whose sum is equal to 90° 
Supplementary Angles:
Pair of angles whose sum is equal to 180°
Identities of Complementary angles are
sin (90° – θ) = cos θ
cos (90° – θ) = sin θ
tan (90° – θ) = cot θ
cot (90° – θ) = tan θ
sec (90° – θ) = cosec θ
cosec (90° – θ) = sec θ
Identities of supplementary angles
sin (180° – θ) = sin θ
cos (180° – θ) = – cos θ
tan (180° – θ) = – tan θ
cot (180° – θ) = – cot θ
sec (180° – θ) = – sec θ
cosec (180° – θ) = – cosec θ
Quadrants of trigonometry
Notice the value of sin 120° cosec 240° tan 210°
Solution:
Here we accept sin 120° cosec 240° tan 210°
We can write as Sin (ninety+30) cosec (180+60) tan (180+30) { equally per the quadrants and trigonometric values }
= Sin 30° × Cosec sixty° × ( Tan 30°)
= 1/2 × 2/√iii × 1√iii
= – i/3
The value of sin 120° cosec 240° tan 210° is – 1/3
Like Questions
Question 1: What is the exact value of sin 270?
Solution:
Here sin is positive only in 1st and 2nd Quadrant.
270° does non lies in 1st and 2d Quadrant.
Therefore sin (360° – θ) = – sin θ
sin (270°) = sin (360° – 90°)
sin (270°) = – sin (90°)
sin (270°) = – 1
So the exact value of sin 270 is i
Question 2: Evaluate (Sin 30° – Sin 90° + 2 Cos 0°) / Tan 30° Tan threescore°?
Solution:
Here we have (Sin 45° – Sin ninety° + 2 Cos 0°) / Tan 45° Tan 60°
Every bit per the trigonometric values
(Sin 45° – Sin xc° +2 Cos 0°) / Tan 45° Tan 60°
= (1/√2 – 1 + 2 × 1) / i × √3
= (1/√2 – 1 + 2) / √3
= (1/√ii + 1) / √three
= (1+√2 / √2) / √iii
Cosec 240
Source: https://www.geeksforgeeks.org/findthevalueofsin120cosec240tan210/