Given that \( \tan \phi=4 \), find the other trigonometric functions. \( \sin \phi=\frac{4 \sqrt{17}}{17} \) (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expressi \( \cos \phi=\frac{\sqrt{17}}{17} \) (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expressi \( \cot \phi=\frac{1}{4} \) (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expressic csc \( \phi=\frac{\sqrt{17}}{4} \) (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expressio sec \( \phi=\square \) (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expressio

1. Find the numerical value of the following trigonometric function: \( \tan 37^{\circ} \)

\( 10 \sqrt { \cot \theta + 2 \cos \theta } \frac { \csc \theta - \sin \theta } { } = \)

Which of the following accurately describes the transformation from \( f(x)=\cos (x) \) and \( g(x)=\cos (-x) \) ? Statement \#1: The function \( g(x) \) is a reflection of \( f(x) \) across the \( y \)-axis. Statement \#2: The function \( g(x) \) is a reflection of \( f(x) \) across the \( x \)-axis. Statement \#3: The function \( g(x) \) is a reflection of \( f(x) \) across \( y=x \). (1 point) Statement \# \( \square \) is correct.

Which of the following statements accurately describes a difference between the graphs of \( f(x)=\sin (x) \) and \( g(x)=\sin (-x) \) ? Statement \#1: If \( (x, y) \) is a point in \( f(x) \), then \( (x,-y) \) is a point in \( g(x) \). Statement \#2: The function \( g(x) \) is the same as \( f(x) \). Statement \#3: If \( (x, y) \) is a point in \( f(x) \), then \( (-x,-y) \) is a point in \( g(x) \). (1 point) Statement \# \( \square \) is correct.

Evaluate the function \( f(x)=-\sin x \) at \( x=\frac{3 \pi}{2} .(1 \) point) \( \left(\frac{3 \pi}{2}, \square\right) \)