3. as the angle θ increases to 90° the value of tan(θ) a. approaches +1. b. decreases rapidly. c. increases rapidly. d. approaches –1.

C. increases rapidly.

Step-by-step 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.

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step-by-step explanation: