Even Functions: cos(-t) = cos(t), sec(-t) = sec(t)
Odd Functions: sin(-t) = -sin(t), tan(-t) = -tan(t), csc(-t) = -csc(t), cot(-t) = -cot(t)
Example: A point P(x, y) is shown on the unit circle corresponding to a real number t. Find the values of the trigonometric functions at t.
A) P(-15/17, 8/17):
Amplitude, Period, and Phase Shift:
y = Asin(Bx):
Financial Management is the process of planning, organizing, directing, and controlling the financial activities of an organization. It involves acquiring funds, utilizing them efficiently, and ensuring maximum returns while minimizing risks.
According to Howard and Upton:
"Financial management is concerned with the application of planning and control functions to the finance function."
Here are the short notes on TDS returns, PAN vs. TAN, and TDS vs. TCS, broken down simply and clearly for your exams.
## (a) Due Date of Furnishing TDS Return
A TDS (Tax Deducted at Source) return is a quarterly statement submitted to the Income Tax Department. It is mandatory for deductors to submit these returns on time to avoid late fees (which run at ₹200 per day under Section 234E).
The financial year is divided into four quarters, and the due date is always the **last day of the month following
Case Study on Repairs and Strengthening of Corrosion-Damaged Buildings
Introduction
Corrosion of reinforcement steel is one of the major causes of deterioration in reinforced concrete structures. It occurs due to the penetration of moisture, oxygen, chlorides, and carbon dioxide into concrete. Corrosion causes expansion of steel, leading to cracking, spalling, reduction in bond strength, and loss of load-carrying capacity. Proper repair and strengthening are necessary to restore structural safety
## 4. Modern Validation APIs (Constraint Validation API)
For advanced tracking and custom error messaging, JavaScript provides the **Constraint Validation API**. This API gives you deep programmatic control over HTML5 validation states.
### Key Properties & Methods
* **element.validity**: An object containing boolean properties describing the validity state of the input.
* validity.valueMissing: True if required but empty.
* validity.typeMismatch: True if the syntax doesn't match the
The **Browser Object Model (BOM)** is what allows JavaScript to talk to the browser about things *outside* the context of the page's actual content. While the DOM deals with the document (HTML, CSS), the BOM deals with everything else—tabs, windows, history, the address bar, and the user's device information.
Here is a comprehensive breakdown of everything BOM, from the window object to how the browser manages state with cookies.
## 1. Introduction to BOM
The BOM is a collection of objects provided
JavaScript uses an **event-driven programming model**. When a user clicks a button, moves the mouse, or types in a form, the browser fires an **event**. JavaScript allows you to intercept these events and execute code in response.
## 1. Core Concepts: Events, Handlers, and Listeners
To work with events, you need to understand three interconnected terms:
* **Event:** The signal that something happened. (e.g., click, keydown, submit, DOMContentLoaded).
* **Event Handler / Listener:** The function
## Introduction to RegExp
A **Regular Expression** (often abbreviated as **RegExp** or **regex**) is a sequence of characters that forms a search pattern. This pattern can be used for text search, text replace, and data validation operations.
In JavaScript, regular expressions are objects. You can create a RegExp object in two ways:
1. **Using a RegExp Literal (Recommended):** The pattern is enclosed between forward slashes.
```javascript
const regex = /pattern/modifiers;
2. **Using the