Question

The point (1, 4) is on the terminal side of angle Θ, in standard position. What are the values of sine, cosine, and tangent of Θ? Make sure to show all work. (10 points)

Answer 1

see the attached figure to better understand the problem

we know that
cos ∅=adjacent side angle ∅/hypotenuse
sin ∅=opposite side angle ∅/hypotenuse
tan ∅=opposite side/adjacent side

in this problem

adjacent side angle ∅=1 units
opposite side angle ∅=4 units

find the hypotenuse
applying the Pythagorean theorem
hypotenuse²=adjacent side²+opposite side²
hypotenuse=√[1²+4²]--------> √17

then
cos ∅=1/√17--------> cos ∅=√17/17

sin ∅=4/√17-----> sin ∅=4√17/17

tan ∅=4/1-------> tan ∅=4