Select the answer which is equivalent to the given expression using your calculator. cot(arccos ((sqrt315)/(18))) (3)/(sqrt315) (sqrt315)/(18) (sqrt315)/(3) (18)/(3)

Question

Select the answer which is equivalent to the given expression using your calculator.  cot(arccos ((sqrt315)/(18)))  (3)/(sqrt315)  (sqrt315)/(18)  (sqrt315)/(3)  (18)/(3)

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Understand relationship between functions: Understand the relationship between cotangent and cosine functions. Cotangent is the reciprocal of the tangent function, and tangent of an angle is the sine divided by the cosine of that angle. Therefore, cotangent of an angle is the cosine divided by the sine of that angle.Evaluate cosine of given angle: Evaluate the cosine of the angle given by arccos((sqrt(315))/(18)). Since arccos((sqrt(315))/(18)) is the angle whose cosine is (sqrt(315))/(18), we can denote this angle as theta for simplicity. So, cos(theta) = (sqrt(315))/(18).Find sine using Pythagorean identity: Find the sine of the angle theta using the Pythagorean identity. The Pythagorean identity states that sin^2(theta) + cos^2(theta) = 1. We already have cos(theta), so we can solve for sin(theta). sin^2(theta) = 1 - cos^2(theta) sin^2(theta) = 1 - ((sqrt(315))/(18))^2 sin^2(theta) = 1 - (315/324) sin^2(theta) = 1 - (35/36) sin^2(theta) = (36/36) - (35/36) sin^2(theta) = (1/36) sin(theta) = sqrt(1/36) sin(theta) = 1/6Calculate cotangent using values: Calculate cot(theta) using the values of sin(theta) and cos(theta). cot(theta) = cos(theta) / sin(theta) cot(theta) = (sqrt(315))/(18) / (1/6) cot(theta) = (sqrt(315))/(18) * (6/1) cot(theta) = (sqrt(315))/(3)

Select the answer which is equivalent to the given expression using your calculator. $\newline$ $\cot \left(\arccos \frac{\sqrt{315}}{18}\right)$ $\newline$ $\frac{3}{\sqrt{315}}$ $\newline$ $\frac{\sqrt{315}}{18}$ $\newline$ $\frac{\sqrt{315}}{3}$ $\newline$ $\frac{18}{3}$

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