Question

If the point (4, 2) is on the terminal side of the angle θ , find each of sin(θ),cos(θ),tan(θ)

sin(θ) =
cos(θ) =
tan(θ) =

Answer 1

\[\sin(\theta)=2/\sqrt(20)\]
\[\cos(\theta)=4/\sqrt(20)\]
\[\tan(\theta)=1/2\]

Answer 2

Assuming that it creates a 90 degree angle with the endpoint (4,2). I believe this is describing just a triangle in the first quadrant.

Answer 3

\[c^2=a^2+b^2=4^2+2^2=20\]\[c=\sqrt{20}\]. Now from the definition of sin, cos and tan:\[\sin \theta=\frac{4}{\sqrt{20}}\]\[\cos \theta=\frac{2}{\sqrt{20}}\]and,\[\tan \theta=\frac{2}{4}=\frac{1}{2}\]

Answer 4

It doesn't need to describe a triangle...the definitions of the trig functions are perfectly general for any degree.

Answer 5

but yeah, the point (4,2) is in the first quadrant so you can interpret it as a right triangle in this example.