Select the answer which is equivalent to the given expression using your calculator. csc(arccos ((sqrt15)/(4))) (4)/(sqrt15) 4 (sqrt15)/(4) sqrt15

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Select the answer which is equivalent to the given expression using your calculator.  csc(arccos ((sqrt15)/(4)))  (4)/(sqrt15) 4  (sqrt15)/(4)  sqrt15

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Understand relationship: Understand the relationship between arccos and cosine. The arccos function is the inverse of the cosine function. This means that if x = arccos(y), then y = cos(x). Therefore, if we have arccos((sqrt15)/4), we can say that cos(theta) = (sqrt15)/4, where theta is the angle whose cosine is (sqrt15)/4.Use Pythagorean identity: Use the Pythagorean identity to find sin(theta). Since cos^2(theta) + sin^2(theta) = 1, we can find sin(theta) by rearranging the identity to sin^2(theta) = 1 - cos^2(theta). We know cos(theta) = (sqrt15)/4, so we can calculate sin(theta) as follows:  sin^2(theta) = 1 - ((sqrt15)/4)^2 sin^2(theta) = 1 - (15/16) sin^2(theta) = (16/16) - (15/16) sin^2(theta) = 1/16 sin(theta) = sqrt(1/16) sin(theta) = 1/4 or sin(theta) = -1/4  Since arccos always gives an angle in the range [0, π], where sine is non-negative, we take the positive value sin(theta) = 1/4.Calculate sin(theta): Calculate csc(theta) using the definition of cosecant. Cosecant is the reciprocal of sine, so csc(theta) = 1/sin(theta). We have found that sin(theta) = 1/4, so:  csc(theta) = 1/(1/4) csc(theta) = 4Conclude csc(theta): Conclude that csc(arccos((sqrt15)/4)) is equivalent to 4. Since we have calculated csc(theta) to be 4, where theta is the angle whose cosine is (sqrt15)/4, we can say that csc(arccos((sqrt15)/4)) = 4.

Select the answer which is equivalent to the given expression using your calculator. $\newline$ $\csc \left(\arccos \frac{\sqrt{15}}{4}\right)$ $\newline$ $\frac{4}{\sqrt{15}}$ $\newline$ $4$ $\newline$ $\frac{\sqrt{15}}{4}$ $\newline$ $\sqrt{15}$

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Select the answer which is equivalent to the given expression using your calculator.\newlinecsc⁡(arccos⁡154) \csc \left(\arccos \frac{\sqrt{15}}{4}\right) csc(arccos415​​)\newline415 \frac{4}{\sqrt{15}} 15​4​\newline444\newline154 \frac{\sqrt{15}}{4} 415​​\newline15 \sqrt{15} 15​

Select the answer which is equivalent to the given expression using your calculator. $\newline$ $\csc \left(\arccos \frac{\sqrt{15}}{4}\right)$ $\newline$ $\frac{4}{\sqrt{15}}$ $\newline$ $4$ $\newline$ $\frac{\sqrt{15}}{4}$ $\newline$ $\sqrt{15}$