If the terminal arm of angle **θ **in standard position passes through the ordered pair (4,5), then...

...Could anyone please leave a detailed response, possibly a picture and graph to show how it would look.

A picture is a great idea, but you can draw it yourself! (Wink)

Draw your axes, and then draw the dot. Draw a vertical line from the dot to the x-axis. Draw a slanty line from the dot to the origin. This gives you a right triangle.

From the x-value of the dot, you know the length, along the x-axis, of the base of the triangle. Label the base with this value.

From the y-value of the dot, you know the length, parallel to the y-axis, of the height of the triangle. Label the height with this value.

From the lengths of the two legs, you can find the length of the hypotenuse by applying the Pythagorean Theorem. Apply the Theorem, and label the hypotenuse with this value.

Label the angle at the origin as \(\displaystyle ``\theta"\).

Read the values of the sine, cosine, tangent, etc of \(\displaystyle \theta\), from your picture. Find the value which matches one of the answer-options. That's your answer! (Clapping)