Cosine geometry definition11/27/2023 To find the value(s) of cosine, it is common to reference a table of cosines, use a calculator, or approximate using the Taylor Series of cosine. The domain of the cosine function is (-∞,∞) and the range of the cosine function is. Unlike the definitions of trigonometric functions based on right triangles, this definition works for any angle, not just acute angles of right triangles, as long as it is within the domain of cos(θ). Meaning that the x-value of any point on the circumference of the unit circle is equal to cos(θ). Thus, we can use the right triangle definition of cosine to determine that The terminal side of the angle is the hypotenuse of the right triangle and is the radius of the unit circle. θ is the angle formed between the initial side of an angle along the x-axis and the terminal side of the angle formed by rotating the ray either clockwise or counterclockwise. In such a triangle, the hypotenuse is the radius of the unit circle, or 1. Given a point (x, y) on the circumference of the unit circle, we can form a right triangle, as shown in the figure. Using the unit circle definitions allows us to extend the domain of trigonometric functions to all real numbers. The right triangle definition of trigonometric functions allows for angles between 0° and 90° (0 and in radians). A unit circle is a circle of radius 1 centered at the origin. Trigonometric functions can also be defined as coordinate values on a unit circle. ![]() The horizontal distance between the person and the plane is about 12.69 miles. ![]() We can then find the horizontal distance, x, using the cosine function: Given the information above, we can form a right triangle such that x is the horizontal distance between the person and the plane, the straight-line distance between the person and the plane is the hypotenuse, and the vertical distance between the terminal ends of x and the hypotenuse forms the right angle of the triangle. ![]() What is the horizontal distance between the plane and the person? The person records an angle of elevation of 25° when the straight-line distance (hypotenuse of the triangle) between the person and the plane is 14 miles.
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