1. **Problem Statement:** We are given that angle $x$ is obtuse, meaning $90^\circ < x < 180^\circ$. We need to determine the truth value of the following statements: a) $\sin x > 0$ b) $\tan x < 0$ c) $\cos x > 0$ 2. **Recall the definitions and signs of trigonometric functions in quadrants:** - An obtuse angle $x$ lies in the second quadrant. - In the second quadrant: - $\sin x$ is positive. - $\cos x$ is negative. - $\tan x = \frac{\sin x}{\cos x}$ is negative (positive divided by negative). 3. **Evaluate each statement:** a) Since $\sin x$ is positive in the second quadrant, $\sin x > 0$ is **true**. b) Since $\tan x$ is negative in the second quadrant, $\tan x < 0$ is **true**. c) Since $\cos x$ is negative in the second quadrant, $\cos x > 0$ is **false**. **Final answers:** a) True b) True c) False