Question

Given the quadrant of q in standard position and a trigonometric function value of q, find the exact value for the indicated function. I,cosq=0.25;tanq

A) 3/4
B) -3/4
C) 4/3
​D) -4/3

Answer 1

To find the exact value of tan(q) given that cos(q) = 0.25 and q lies in a particular quadrant, substitute the known values in the Pythagorean Identity and evaluate the trigonometric function.

Step-by-step explanation:

To find the exact value of tan(q) given that cos(q) = 0.25 and q lies in a particular quadrant, we can use the identity tan(q) = sin(q)/cos(q). Since we know cos(q) = 0.25, we need to find sin(q) to evaluate tan(q). We can use the Pythagorean Identity sin^2(q) + cos^2(q) = 1 to find sin(q).

Given cos(q) = 0.25, we can substitute it in the Pythagorean Identity to get sin^2(q) + 0.25^2 = 1. Simplifying this equation, we have sin^2(q) = 1 - 0.25^2 = 0.9375. Taking the square root of both sides, we get sin(q) = ± √0.9375.

Now, tan(q) = sin(q)/cos(q). Substituting the values we found, we have tan(q) = (± √0.9375)/0.25. This can be simplified to ± (4/3).