a concave lens has focal length of 20cm. at what distance should an object be placed from the lens so that it forms an real image at 20cm from the lens?
Answers
Trigonometry Values
Trigonometry values of different ratios, such as sine, cosine, tangent, secant, cotangent, and cosecant, deal with the measurement of lengths and angles of the right-angle triangle. The values of trigonometric functions for 0°, 30°, 45°, 60° and 90° are commonly used to solve trigonometry problems.
Trigonometry values are all about the study of standard angles for a given triangle with respect to trigonometric ratios. The word ‘trigon’ means triangle and ‘metron’ means ‘measurement’. It’s one of the major concepts and part of geometry, where the relationship between angles and sides of a triangle is explained.
Maths is an important subject, where we learn about different types of calculations and logic applied in our day-to-day life. Trigonometry basics are widely explained in student’s academic classes of 9 and 10. Here, you will learn about different trigonometric ratios and formulas. Also, solve problems based on these formulas and identities to understand the fundamentals of trigonometry in a better way.
Trigonometry Values Table
Let us learn, trigonometry values for angles 0°, 30°, 45°, 60° and 90°, with respect to sin, cos, tan, cot, sec, cosec functions, taking an example of the right-angle triangle.
Angle
00
300450600
900
Sin θ01/21/√2√3/21Cos θ1√3/21/√21/20Tan θ01/√31√3∞Cot θ∞√311/√30Sec θ12/√3√22∞Cosec θ∞2√22/√31
Suppose ABC is a right-angled triangle, right-angled at B. This triangle has a hypotenuse AC, an adjacent side AB which is adjacent to ∠θ and a perpendicular BC opposite to ∠θ.

Trigonometry values are based on three major trigonometric ratios, Sine, Cosine, and Tangent.
Sine or sin θ = Side opposite to θ / Hypotenuse = BC / AC
Cosines or cos θ = Adjacent side to θ / Hypotenuse = AB / AC
Tangent or tan θ =Side opposite to θ / Adjacent side to θ = BC / AB
Similarly, we can write the trigonometric values for Reciprocal properties, Sec, Cosec and Cot ratios.
Sec θ = 1/Cos θ = Hypotenuse / Adjacent side to angle θ = AC / AB
Cosec θ = 1/Sin θ = Hypotenuse / Side opposite to angle θ = AC / BC
Cot θ = 1/tan θ = Adjacent side to angle θ / Side opposite to angle θ = AB / BC
Also,
Sec θ . Cos θ =1
Cosec θ . Sin θ =1
Cot θ . Tan θ =1
Trigonometry Ratios Formula
Tan θ = sin θ/cos θ
Cot θ = cos θ/sin θ
Sin θ = 1/cosec θ
Cos θ = sin θ/tan θ = 1/sec θ
Sec θ = tan θ/sin θ = 1/cos θ
Cosec θ = 1/sin θ
Also,
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
Trigonometry Examples
Problem:
Find the value of sin(90-45)°.
Solution:
sin(90-45)° = cos 45° = 1/√2
Problem:
If tan θ = 4 and sin θ = 6. Then find the value of cos θ.
Solution:
We know, cos θ = sin θ/ tan θ
Therefore, cos θ = 6/4 = 3/2
Keep learning Maths with us and download BYJU’S- The learning App, for interactive videos.
MATHS Related LinksTrigonometric FunctionsTrigonometry TableTrigonometry FormulasTrigonometric IdentitiesInverse Trigonometric FunctionsTrigonometric Addition Formulas
Test your knowledge on Trigonometry Values

Put your understanding of this concept to test by answering a few MCQs. Click ‘Start Quiz’ to begin!
Select the correct answer and click on the “Finish” button
Check your score and answers at the end of the quiz
Start Quiz
Trigonometry Values
Trigonometry values of different ratios, such as sine, cosine, tangent, secant, cotangent, and cosecant, deal with the measurement of lengths and angles of the right-angle triangle. The values of trigonometric functions for 0°, 30°, 45°, 60° and 90° are commonly used to solve trigonometry problems.
Trigonometry values are all about the study of standard angles for a given triangle with respect to trigonometric ratios. The word ‘trigon’ means triangle and ‘metron’ means ‘measurement’. It’s one of the major concepts and part of geometry, where the relationship between angles and sides of a triangle is explained.
Maths is an important subject, where we learn about different types of calculations and logic applied in our day-to-day life. Trigonometry basics are widely explained in student’s academic classes of 9 and 10. Here, you will learn about different trigonometric ratios and formulas. Also, solve problems based on these formulas and identities to understand the fundamentals of trigonometry in a better way.
Trigonometry Values Table
Let us learn, trigonometry values for angles 0°, 30°, 45°, 60° and 90°, with respect to sin, cos, tan, cot, sec, cosec functions, taking an example of the right-angle triangle.
Angle
00
300450600
900
Sin θ01/21/√2√3/21Cos θ1√3/21/√21/20Tan θ01/√31√3∞Cot θ∞√311/√30Sec θ12/√3√22∞Cosec θ∞2√22/√31
Suppose ABC is a right-angled triangle, right-angled at B. This triangle has a hypotenuse AC, an adjacent side AB which is adjacent to ∠θ and a perpendicular BC opposite to ∠θ.

Trigonometry values are based on three major trigonometric ratios, Sine, Cosine, and Tangent.
Sine or sin θ = Side opposite to θ / Hypotenuse = BC / AC
Cosines or cos θ = Adjacent side to θ / Hypotenuse = AB / AC
Tangent or tan θ =Side opposite to θ / Adjacent side to θ = BC / AB
Similarly, we can write the trigonometric values for Reciprocal properties, Sec, Cosec and Cot ratios.
Sec θ = 1/Cos θ = Hypotenuse / Adjacent side to angle θ = AC / AB
Cosec θ = 1/Sin θ = Hypotenuse / Side opposite to angle θ = AC / BC
Cot θ = 1/tan θ = Adjacent side to angle θ / Side opposite to angle θ = AB / BC
Also,
Sec θ . Cos θ =1
Cosec θ . Sin θ =1
Cot θ . Tan θ =1
Trigonometry Ratios Formula
Tan θ = sin θ/cos θ
Cot θ = cos θ/sin θ
Sin θ = 1/cosec θ
Cos θ = sin θ/tan θ = 1/sec θ
Sec θ = tan θ/sin θ = 1/cos θ
Cosec θ = 1/sin θ
Also,
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
Trigonometry Examples
Problem:
Find the value of sin(90-45)°.
Solution:
sin(90-45)° = cos 45° = 1/√2
Problem:
If tan θ = 4 and sin θ = 6. Then find the value of cos θ.
Solution:
We know, cos θ = sin θ/ tan θ
Therefore, cos θ = 6/4 = 3/2
Keep learning Maths with us and download BYJU’S- The learning App, for interactive videos.
MATHS Related LinksTrigonometric FunctionsTrigonometry TableTrigonometry FormulasTrigonometric IdentitiesInverse Trigonometric FunctionsTrigonometric Addition Formulas
Test your knowledge on Trigonometry Values

Put your understanding of this concept to test by answering a few MCQs. Click ‘Start Quiz’ to begin!
Select the correct answer and click on the “Finish” button
Check your score and answers at the end of the quiz
Start Quiz