Use an inverse trigonometric function to write 𝜃 as a function of x.

Question

right triangle

hyp= 6

opp= x+3

adj=?

Answer 1

Here is a sketch:

Use the Pythagorean Theorem to find the adj:

(adj)² + (x + 3)² = 6²

(adj)² = 36 - (x + 3)²

adj = √(36 - (x + 3)²)

To write theta as a function of x using an inverse trig function, you could pick any of them. I'll choose arcsin:

start with sin(θ) = opp/hyp

sin(θ) = (x + 3)/6

Now take the arcsine (or sin^-1) of both sides:

sin^-1(sin(θ)) = sin^-1((x + 3)/6)

θ = sin^-1((x + 3)/6)

θ(x) = arcsin((x + 3)/6)