Use the given information to determine the values of the...

Use the given information to determine the values of the remaining five trigonometric functions. (Assume that all of the angles are acute. When radicals appear in a denominator, rationalize the denominator.
$$\cos A=8 / 17$$

Key Concepts

Pythagorean Identity

This is a fundamental relation in trigonometry stating that for any angle, the square of the sine plus the square of the cosine equals one. It is used to calculate an unknown trigonometric function when the value of another is given, forming the basis for many trigonometric calculations.

Reciprocal Trigonometric Functions

Each of the primary trigonometric functions has a corresponding reciprocal function: sine with cosecant, cosine with secant, and tangent with cotangent. Understanding these relationships allows one to express and compute various trigonometric ratios in alternative forms, which can be useful for solving different types of problems.

Definition of Trigonometric Ratios

Trigonometric ratios such as sine, cosine, and tangent are defined based on the ratios of specific sides of a right-angled triangle relative to a given acute angle. These definitions provide the foundational framework for computing and interrelating the six trigonometric functions.

Rationalization of Denominators

This algebraic process involves rewriting a fraction so that there are no radicals in its denominator. Rationalizing denominators is important in trigonometry to present answers in their simplest and most standardized form, especially when square roots are involved.

Properties of Acute Angles

In trigonometry, acute angles (those less than 90 degrees) have the characteristic that all six trigonometric functions are positive. This property simplifies calculations and ensures consistency when applying identities and ratio definitions within right-angled triangles.

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