Find the exact values of the trigonometric functions for the acute angle θ. cot θ=(7)/(24)

Name: Problem 20, Chapter 5: Precalculus: Functions and Graphs
Uploaded: 2021-05-02T16:45:56-08:00
Duration: 3 min 17 s
Channel: Raushan Kumar
Description: Find the exact values of the trigonometric functions for the acute angle θ. cot θ=(7)/(24)

step 1 we are going to do problem number 20 so in this question the value of chord theta is given that

Find the exact values of the trigonometric functions for the...

Key Concepts

Trigonometric Functions

Trigonometric functions, such as sine, cosine, tangent, cotangent, secant, and cosecant, are mathematical functions that relate the angles of a triangle to the ratios of its sides. They are fundamental in studying the properties of triangles and periodic phenomena, and their definitions arise naturally in the context of the unit circle and right triangle geometry.

Right Triangle Trigonometry

Right triangle trigonometry involves studying triangles with one 90-degree angle, where the ratios of the sides relative to an acute angle define the trigonometric functions. When given a ratio like cotangent, the sides of the triangle can be represented in terms of adjacent and opposite sides, facilitating the use of these ratios to compute exact trigonometric values.

Pythagorean Theorem

The Pythagorean theorem is a central concept in trigonometry that relates the lengths of the sides of a right triangle. It states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. This theorem is crucial for finding the missing side of a triangle when two sides are known, and thereby calculating the other trigonometric functions.

Reciprocal Identities

Reciprocal identities express the relationships between trigonometric functions and their reciprocals. For instance, the cotangent is the reciprocal of the tangent, and sine and cosine have reciprocals cosecant and secant, respectively. These identities allow for conversion between different functions, simplifying the computation of exact values in trigonometric problems.

Exact Value Computation

Computing the exact values of trigonometric functions involves using known ratios and relationships, often derived from constructing a right triangle based on provided trigonometric ratios. In this context, with a given cotangent value, the use of side ratios and the Pythagorean theorem enables the determination of sine, cosine, tangent, and their reciprocals without resorting to decimal approximations.

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