Final answer:
To solve for the value of tan 6 between 0° and 90° if cos 0 = 0.25, use the trigonometric identity tan x = sin x / cos x. First, find the value of sin 0 using the Pythagorean identity sin² x + cos² x = 1. Then substitute the values of sin 0 and cos 0 into the trigonometric identity tan x = sin x / cos x to find the value of tan 6.
Step-by-step explanation:
To solve for the value of tan 6 between 0° and 90° if cos 0 = 0.25, we can use the trigonometric identity tan x = sin x / cos x. Since we know the value of cos 0, we can find the value of sin 0 using the Pythagorean identity sin² x + cos² x = 1. Then we can substitute these values into the trigonometric identity tan x = sin x / cos x to find the value of tan 6.
First, find the value of sin 0:
sin² 0 + cos² 0 = 1
sin² 0 + 0.25² = 1
sin² 0 + 0.0625 = 1
sin² 0 = 1 - 0.0625
sin² 0 = 0.9375
sin 0 = √0.9375
sin 0 ≈ 0.96825
Now substitute the values of sin 0 and cos 0 into the trigonometric identity tan x = sin x / cos x to find the value of tan 6:
tan 6 = sin 6 / cos 6
tan 6 = (0.96825) / (0.25)
tan 6 ≈ 3.873