Question

Given the quadrant of q in standard and a trigonometric function value of q, find the exact value for the indicated function.

Quadrant: III, cos(q) = -1.25; find tan(q).

Answer 1

In the third quadrant with a cosine value of -1.25, the exact value of tangent is sqrt(0.45) / 1.25.

Step-by-step explanation:

To find the exact value of the tangent function, we need to use the given cosine value and the quadrant of the angle. In the third quadrant, cosine is negative and tangent is positive. Since cosine is -1.25, we can use the Pythagorean identity to find the sine value: sin(q) = sqrt(1 - cos^2(q)).

solve for the sine: sin(q) = sqrt(1 - (-1.25)^2) = sqrt(1 - 1.5625) = sqrt(-0.5625).

However, the sine of an angle cannot be negative in the third quadrant, so we need to use the negative square root: sin(q) = -sqrt(0.5625).

Finally, we can find the tangent value by dividing the sine by the cosine: tan(q) = sin(q) /cos(q) = -sqrt(0.5625) / -1.25 = sqrt(0.5625) / 1.25 = sqrt(0.45) / 1.25.