Answer: the simplified form of sec(Q) is sqrt(24/7).
Step-by-step explanation: The equation secant of angle Q is equal to two multiplied by the square root of six and divided by nine.
In order to reduce the complexity of the given mathematical expression, it is possible to employ the fundamental definition of secant, which states that:
The trigonometric identity denoted as sec(Q) equals the reciprocal of the cosine function evaluated at the angle Q. More precisely, sec(Q) = 1 / cos(Q).
The value of cos(Q) may be determined through the utilization of the Pythagorean identity.
The present mathematical equation demonstrates a fundamental identity in trigonometry, wherein the squares of the sine and cosine functions are summed to equal one. Written symbolically, the equation can be expressed as sin^2(Q) + cos^2(Q) = 1.
Given the condition that sec(Q) is positive, it is ascertainable that Q is situated within the first or fourth quadrant, wherein the cosine of Q is likewise positive. Consequently, the derivation for the solution of the cosine of the angle Q can be expressed as follows:
The trigonometric identity expressed as cos(Q) = sqrt(1 - sin^2(Q)) is a fundamental result in the field of mathematics. This particular equation provides a relationship between the cosine and sine functions of angle Q. Specifically, it states that the cosine of an angle Q is equal to the square root of one minus the sine squared of the same angle Q. The use of such identities is common in mathematical analysis and applied sciences, where it allows for efficient manipulation of trigonometric functions and the mathematical modeling of a variety of physical phenomena.
The following mathematical expression can be written in an academic style: Cosine of angle Q can be expressed as the square root of one minus the square of nine divided by twice the square root of six, i.e., cos(Q) = √(1 - (9/2√6)^2), while substituting the value of sine of angle Q as being equal to nine divided by twice the square root of six (i.e., sin(Q) = 9/2√6).
The mathematical expression cos(Q) = sqrt(1 - (81/24)) may be represented in a more academic manner. Specifically, it may be articulated as follows: the cosine of angle Q is equivalent to the square root of one subtracted by the quotient of 81 and 24. This revision lends itself to a more formal and precise mode of communication, which is characteristic of academic writing.
The mathematical expression cos(Q) = √(7/24) can be represented in a formal and academic manner.
The value of secant of angle Q can now be determined as:
The trigonometric function defining the secant of an angle Q is expressed as sec(Q) = 1/cos(Q).
The trigonometric function, sec(Q), can be expressed as the reciprocal of the square root of 7/24.
The mathematical statement, sec(Q) = sqrt(24/7), can be expressed in a formal and academic manner as follows. The reciprocal of the cosine function of the angle Q is equivalent to the square root of the fraction 24 over 7.