# Trigonometry Formulas Class 10

Trigonometry formulas Class 10 are related to the relationships between the sides and angles of a right-angled triangle. Trigonometric ratios are ratios of sides of the right triangle. These formulas are quite important to find the angles and the length of sides by applying trigonometric ratios. Apart from mathematics, class 10 trigonometry formulas hold great significance in various subjects like architecture, engineering, astronomy, geography, music, electronics, civil engineering, oceanography, image compression, chemistry and medical imaging. Read along to know more about important class 10 trigonometry formulas, their practical applications and their importance.

## List of Trigonometry Formulas Class 10

- sin A = Perpendicular/ Hypotenuse
- cos A = Base/ Hypotenuse
- tan A = Perpendicular/ Base
- cos
^{2}A + sin^{2}A = 1 - 1 + tan
^{2}A = sec^{2}A - cot
^{2 }A + 1 = cosec^{2}A - sin(90∘−A) = cos A
- cos(90∘−A) = sin A
- tan(90∘−A) = cot A
- cot(90∘−A) = tan A
- sec(90∘−A) = cosec A
- cosec(90∘−A) = sec A
- sin² θ + cos² θ = 1
- sin² θ = 1 – cos² θ
- cos² θ = 1 – sin² θ
- cosec² θ – cot² θ = 1
- cosec² θ = 1 + cot² θ
- cot² θ = cosec² θ – 1
- sec² θ – tan² θ = 1
- sec² θ = 1 + tan² θ
- tan² θ = sec² θ – 1
- sin θ cosec θ = 1
- cos θ sec θ = 1
- tan θ cot θ = 1

## Applications of Trigonometry Formulas Class 10

Trigonometry formulas Class 10 are widely applied in construction work, mechanical engineering, designing, seismology, oceanography, phonetics, architecture, etc. Many routine calculations in the various fields use trigonometry formulas. Here are some uses of class 10 trigonometry formulas:

- Trigonometry formulas are applied to evaluate the height of buildings, mountains, towers, angles of elevations and slopes.
- Another real life use of trigonometry formulas is calculating the distance between the ship and the seashore.
- These formulas help astronauts to determine the speed and altitude of celestial bodies.
- Representation of various physical quantities like oscillations, electromagnetic waves, mechanical waves, etc., has a lot of application of trigonometric formulas.
- Trigonometry formulas are applied in solar cell panels to calculate the sun height angle to determine power output at different angles.

## Tips to Memorize Trigonometry Formulas Class 10

- The first step towards memorizing class 10 trigonometry formulas is to clearly understand the terms related to ratios and angles. Students should form an accurate understanding of each and every trigonometry concept to apply these formulas.
- Students should try to eliminate all their doubts and errors by referring to the interactive expert-led study material online or by reaching out to their concerned teacher.
- A step-by-step derivation of the trigonometry formulas is an excellent approach to enhance the foundational knowledge of all underlying concepts.

- After having a crystal-clear knowledge of the terms used in formulas, students can try to use some fun tricks like phrases to remember them better.
- Students can download and set the trigonometry formulas images as wallpaper on their devices which will help them ensure a quick revision while they use their mobiles, tablets or laptops.

- Students should practice lots of problems and examples given in the textbook. It will provide optimal coverage of the usage of formulas in different contexts.

## Trigonometry Formula Class 10 Examples

**Example:** If sec 2A = cosec (A – 60°), where 4A is an acute angle, find the value of A.

**Solution:** In order to solve this question we can use the trigonometric ratios of complementary angles.

Given equation is, sec 2A = cosec (A - 60°)

We know that, sec A = cosec (90° - A)

By using this property in the given equation we get:

cosec (90° - 2A) = cosec (A - 60°)

90° - 2A = A - 60°

3A = 150°

A = 150°/3

A = 50°

Students can download the printable **Maths Formulas Class 10** sheet from below.

## FAQs On Trigonometry Formulas Class 10

### What are the Important Trigonometry Formulas in Class 10?

The important trigonometry formulas Class 10 are listed below

- sin (90∘−A) = cos A
- cos (90∘−A) = sin A
- tan (90∘−A) = cot A
- cot (90∘−A) = tan A
- sec (90∘−A) = cosec A
- cosec (90∘−A) = sec A
- sin² θ + cos² θ = 1
- sin² θ = 1 – cos² θ
- cos² θ = 1 – sin² θ
- cosec² θ – cot² θ = 1
- cosec² θ = 1 + cot² θ
- cot² θ = cosec² θ – 1
- sec² θ – tan² θ = 1
- sec² θ = 1 + tan² θ
- tan² θ = sec² θ – 1
- sin θ cosec θ = 1
- cos θ sec θ = 1
- tan θ cot θ = 1

### What are the Real-Life Applications of Trigonometry Formulas Class 10?

Trigonometry formulas class 10 are applied in construction work, mechanical engineering, designing, seismology, oceanography, phonetics, architecture, etc. Many routine calculations like measuring the height of buildings, mountains, towers, angles of elevations and slopes see the use of trigonometry formulas.

### Why is it Important to Practice Questions Based on Trigonometry Formulas Class 10?

Solving questions based on trigonometry formulas class 10 will enable students to understand the use of trigonometry in various contexts. It will also help them prepare effectively for various competitive exams and academic tests. Students will be able to build problem-solving skills and form a core conceptual understanding of this topic by practicing practical problems based on these formulas.

### How to Memorize Trigonometry Formulas Class 10?

Memorizing trigonometry formulas class 10 requires practice and perseverance. With the practice of a wide range of questions based on this formula, students will gain deep knowledge of the core concepts. They will also learn some creative ways to memorize formulas and important theorems. It will enable them to use their knowledge of formulas in various situations, which is highly useful for facing competitive exams.

### How Many Formulas are there in Trigonometry Class 10 Maths?

There are around 20 main formulas present in trigonometry class 10 maths. Students are advised to thoroughly go through each and every formula provided in the list to have a clear idea of the terms and concepts applied in this topic. This is also helpful in solving various types of problems covered under this topic.

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