Question

As the angle θ increases to 90° the value of tan(θ)

A. decreases rapidly.
B. approaches +1.
C. increases rapidly.
D. approaches –1.

Answer 1

C. increases rapidly.

Explanation:

tan(θ) = sin(θ)/cos(θ)

Now, when sin 90 = 1

and cos 90 = 0

so, tan(90) = 1/0 = not defined.

(1/0 is infinity and its value is not defined)

So, when angle θ increases to 90°, then the value of tan(θ) increases rapidly, as shown in the figure below.