The sine function, denoted as sin(a), is a fundamental function in trigonometry that describes the ratio of the length of the side opposite an angle a in a right-angled triangle to the length of the hypotenuse of the triangle. When expressed as a fraction, sin(a) is represented as: sin(a) = \frac{opposite}{hypotenuse} To simplify this concept … Read more
To find the polynomial function of lowest degree with a lead coefficient of 1 and roots 1 and 1i, we first need to note that polynomials with real coefficients require complex roots to be in conjugate pairs. Thus, if 1i is a root, its conjugate, -1i, must also be a root. The roots of the … Read more
To solve for sin(θ) given the conditions, let’s first clarify what we know: cos(5) = 13: This part of the statement is not clear as the cosine function ranges from -1 to 1. Such a value is not valid in the context of trigonometric functions. tan(θ) = 0: The tangent of an angle is zero … Read more
Rewriting the Expression To rewrite the given expression the cube root of 2 to the seventh power as a rational exponent, we’ll follow these steps: Step 1: Understand the Fractional Exponent The cube root of a number can be expressed as a rational exponent. In mathematical terms, the cube root of any number x is … Read more
To find a point on a line and determine its slope, you’ll first need an equation of the line. The most common forms of a line’s equation are the slope-intercept form, given as y = mx + b, where m represents the slope, and b is the y-intercept. Alternatively, you might encounter the point-slope form, … Read more
To find the value of f(g(2)), we need to perform the following steps: Compute g(2): Given the function g(x) = x + 2, we substitute x with 2: g(2) = 2 + 2 = 4 Compute f(g(2)) or f(4): The function f(x) = 2x + 3x simplifies to f(x) = 5x. Now, we will substitute … Read more
The sequence in question consists of letters that have specific characteristics based on their shapes when written in uppercase. Each of these letters contains straight lines or angles. To break down the sequence: A
To evaluate the function rule y = 15 – 3x for the value of x = 3, we need to substitute x with 3 in the equation. Here’s the step-by-step breakdown: Start with the original function: y = 15 – 3x. Substitute x with 3: y = 15 – 3(3). Now calculate 3(3): 3(3) = … Read more
To find the values of h8 when given the equation h8 = 8 cos(8), we can follow these steps: Understand the Equation: The equation tells us that h8 is equal to 8 times the cosine of 8. Here, we need to clarify that the ‘8’ inside the cosine function is in radians unless otherwise specified. … Read more