devyy The cosine function, commonly written as cos(θ), is a fundamental function in trigonometry that describes the relationship between the adjacent side and the hypotenuse of a right triangle. The values of the cosine function correspond to specific angles, which are often represented in degrees. Here are some key angles and their cosine values: 0°: cos(0°) … Read more
When we talk about powers in mathematics, we’re referring to an expression that represents repeated multiplication. In this case, the expression 10 to the 5th power, or 105, means that we multiply the number 10 by itself a total of five times. To break it down, 105 can be calculated as follows: 10 × 10 … Read more
Integrating the function sin(x) is a fundamental concept in calculus. The integral of sin(x) is often one of the first integrals learned because it provides essential insights into trigonometric functions and their properties regarding area under curves. Here’s a detailed breakdown of the steps involved in this integration: Understand the Integral: The indefinite integral of … Read more
To convert the improper fraction 29/5 into a mixed number, follow these steps: **Divide the numerator by the denominator**: In this case, divide 29 by 5. When you perform this division, you get: 29 ÷ 5 = 5 with a remainder of 4. **Write the whole number**: The quotient (5) is the whole number part … Read more
The factorial of a number is the product of all positive integers up to that number. For instance, the factorial of 5 (written as 5!) is calculated as: 5! = 5 × 4 × 3 × 2 × 1 = 120 Now, let’s calculate the factorial of 20, which is written as 20!. It’s the … Read more
Multiplying square roots can seem tricky at first, but it’s quite straightforward once you understand the basic principles involved. Here’s a step-by-step guide on how to do it: Step 1: Understand the Property of Square Roots The key property that you need to know is that the square root of a product is equal to … Read more
To convert the improper fraction 17/8 into a mixed number, you follow a simple process: Divide the numerator by the denominator: In this case, you divide 17 (the numerator) by 8 (the denominator). This gives you a quotient of 2. Find the remainder: Next, calculate the remainder of 17 divided by 8. Since 8 goes … Read more
To determine the new coordinates of the point (17, 14) after a rotation of 270 degrees counterclockwise about the origin, we can use the standard rotation formulas. When a point (x, y) is rotated by an angle θ, the new coordinates (x’, y’) can be calculated by: x’ = x * cos(θ) – y * … Read more
To convert the fraction 13/9 into a mixed number, follow these steps: Divide the numerator by the denominator: In this case, divide 13 (the numerator) by 9 (the denominator). When you do this division, you find that: 13 ÷ 9 = 1 with a remainder of 4. Determine the whole number and remainder: The result … Read more
In mathematics, any non-zero number raised to the power of 0 is always equal to 1. This rule applies to all numbers, including 7. Therefore, 7 to the power of 0 is 1. This concept can be understood through the rules of exponents. When you raise a number to a power, you are essentially multiplying … Read more