Question

Consider this equation. cos ⁡ ( θ ) = - 7 8 if θ is an angle in quadrant iii, what is the value of tan ⁡ ( θ ) ? a. 15 7 b. - 15 7 c. - 15 8 d.

Answer 1

In quadrant III, if cos(θ) = -7/8, the value of tan(θ) is -15/7.

Step-by-step explanation:

To find the value of tan(θ) when cos(θ) = -7/8 in quadrant III, we can use the trigonometric identity tan(θ) = sin(θ)/cos(θ).

In quadrant III, cos(θ) is negative and sin(θ) is also negative.

Since we have cos(θ) = -7/8, we can write sin(θ) = √(1 - cos^2(θ)) to find the value of sin(θ).

Using these values, we can calculate tan(θ) = sin(θ)/cos(θ).

Therefore, the value of tan(θ) is 15/7 or -15/7.