# Trigonometric Formulas for Class 12

Trigonometric formulas for class 12 involve the use of trigonometric functions and trigonometric identities. With the introduction of inverse trigonometry functions and their properties, it often becomes confusing for students to comprehend these concepts. So, it is essential to gain clarity on these formulas before applying them. This article has summarized all important trigonometric formulas for class 12 that students should go through and memorize.

## List of Trigonometric Formulas for Class 12

- Range of sine function : R→ [- 1, 1]
- Range of cosine function : R → [- 1, 1]
- Range of tangent function : R – { x : x = (2n + 1) 2 π , n ∈ Z} →R
- Principal branch of inverse of Sine function : → [−π/2, π/2 ]
- Principal branch of inverse of Cosine function : → [0, π ]
- Principal branch of inverse of Tangent function : → [-π/2, π/2 ]
- sin
^{-1}(-x) = – sin^{-1}x - tan
^{-1}(-x) = - tan^{-1}x - tan
^{-1}x + cot^{-1}x = 2 π - sin
^{-1}(sin x) = x

## Applications of Trigonometric Formulas for Class 12

Trigonometric formulas find their place in several domains. Some of the examples of the application of trigonometry formulas for class 12 are given below:

- Trigonometric formulas for class 12 aid in determining the behavior as well as the size of a variety of sea creatures. For example, the photosynthesis of algae can be found out using information about the light falling under the water at a specific angle.

- Engineers use trigonometry to design and analyze structures. Thus, whether it's civil, chemical, electrical engineering or aerospace trigonometric formulas are used everywhere.
- Designing various instruments and tools also requires trigonometric calculations and analysis.

## Tips to Memorize Trigonometric Formulas for Class 12

To help students memorize the trigonometric formulas for class 12 below-mentioned are some useful tips.

- Students must practice the formulas along with their logical explanations to understand their applications. Once the logic is clear, they will understand to apply them in different contexts.
- Students can find various online resources like formula sheets, simulations and worksheets to memorize these formulas. They can also save the formula images on their devices to revise them.
- It is important that students clear all their doubts related to these formulas before applying them. They can take the help of their teachers and parents in clearing all their doubts.

## Trigonometric Formulas for Class 12 Examples

**Example 1:** Find the value of sin^{-1} (sin 4π/5 )?

**Solution:** Using formula, sin^{-1} (sin x) = x but the principal value branch of sin–1 (x) is [-π/2, π/2] and 4π/5 does not fall within [-π/2, π/2]

However, by using identity sin(π−x) = sinx, we can write sin 4π/5 as sin (π - 4π/5) = sin (π/5)

= sin^{-1} (sin π/5 ) and π/5 ∈ [-π/2, π/2]

= π/5

**Example 2:** Find the value of cos(sin^{-1} x + cos^{-1} x)?

**Solution:** We know that,

sin^{-1} x + cos^{-1} x = π/2

So, cos (sin^{-1} x + cos^{-1} x) = cos (π/2)

Thus,cos (π/2) = 0

Students can download the printable **Maths Formulas Class 12** sheet from below.

## FAQs on Trigonometric Formulas for Class 12

### What are the Important Trigonometric Formulas for Class 12?

The important Trigonometric Formulas for Class 12 are as:

- Range of sine function : R→ [- 1, 1]
- Range of cosine function : R → [- 1, 1]
- Range of tangent function : R – { x : x = (2n + 1) 2 π , n ∈ Z} →R
- Principal branch of inverse of Sine function : → [-π/2, π/2]
- Principal branch of inverse of Cosine function : → [0, π ]
- Principal branch of inverse of Tangent function : → [-π/2, π/2]
- sin
^{-1}(-x) = - sin^{-1}x - tan
^{-1}(-x) = - tan^{-1}x - tan
^{-1}x + cot^{-1}x = 2 π - sin
^{-1}(sin x) = x

### What are the Important Applications of Trigonometric Formulas for Class 12?

The applications of trigonometric formulas for class 12 can be seen in various engineering fields and other subjects. These formulas are widely applied in real life for measuring angles and distances for critical problem-solving.

### Why is it Important to Practice Problems Based on Trigonometric Formulas for Class 12?

Solving problems based on trigonometric formulas for class 12 will enable students to work with the basic properties of trigonometric functions. Students must go through the examples and list of formulas provided in the article to get a hold of applying trigonometric formulas in solving problems.

### How Many Formulas are There in Trigonometric Formulas for Class 12?

There are around ten formulas in Trigonometric Formulas for Class 12 that cover the topic of domain and ranges in inverse trigonometric functions and their properties. All of these formulas are widely used in various sciences to obtain information and data.

### How can I Memorize Trigonometric Formulas for Class 12?

Here are some tips that can help students memorize the Trigonometric Formulas for Class 12 as elaborated in this article are as below:

- Students should practice writing down formulas and their explanations so that they understand the logic behind them.
- Trigonometric formulas can also be learned quickly by framing any unique term or phrase from the formulas' initials.
- Students can use the formula images as wallpaper on their smartphones and desktops. It will help to visualize formulas and remember them quickly.

visual curriculum