Identify what angle, $\(\theta\)$ , satisfies the following conditions.
$\(\tan\)\(\theta\)=-1$; $\(\cos\)\(\theta\)$ > $0$

• A. 45°
• B. 135°
• C. 315°
• D. 330°

Answer: (C)

Verified step by step guidance

1. Understand that the problem is asking for an angle θ where tan(θ) = -1 and cos(θ) > 0.
2. Recall that the tangent function, tan(θ), is negative in the second and fourth quadrants of the unit circle.
3. Recognize that cos(θ) > 0 indicates that θ must be in the fourth quadrant, as cosine is positive in the first and fourth quadrants.
4. Identify that in the fourth quadrant, the reference angle for tan(θ) = -1 is 45°, which corresponds to an angle of 315°.
5. Verify that 315° satisfies both conditions: tan(315°) = -1 and cos(315°) > 0.