Identify what angle, θ \theta θ , satisfies the following conditions. tan θ = − 1 \tan\theta=-1 tan θ = − 1 ; cos θ \cos\theta cos θ > 0 0 0

In this problem we're asked to identify which angle theta satisfies the following conditions, and the conditions that we're given here are that the tangent of theta is equal to negative one and the cosine of theta is greater than 0. Now we want to find an angle that satisfies both of these conditions, but let's first take a look at this first condition, the tangent of theta being equal to negative one. Now looking at my unit circle here, I look at my tangent values and I see that for 135 degrees, my tangent value is indeed negative one. Now continuing around my unit circle and ending up in quadrant 4, I see that for 315 degrees, my tangent is also equal to negative one. So there are two possible answers here either 135 degrees or 315 degrees. This is where our second condition comes in. Now our second condition here is that the cosine of theta has to be positive or greater than 0. Now in my second quadrant, quadrant 2, my cosine value, this first value is negative. So this cannot be my answer. My answer is not 135 degrees. Now taking a look at our other angle to make sure that it does satisfy that other condition before just saying that's our answer, I come down here to my cosine value of root 2 over 2, which is a positive value greater than 0. And I remember that in this quadrant 4, cosine is actually the only positive trig function. So this is my final answer. That 315 degrees, the tangent is equal to negative one, and the cosine is greater than 0. So my angle here theta is 315 degrees and I'm done here. Thanks for watching and I'll see you in the next one.

3. Unit Circle

Reference Angles

Trigonometry

3. Unit Circle

Reference Angles

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Multiple Choice

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

45°

135°

315°

330°

Verified step by step guidance

Understand that the problem is asking for an angle θ where tan(θ) = -1 and cos(θ) > 0.

Recall that the tangent function, tan(θ), is negative in the second and fourth quadrants of the unit circle.

Since cos(θ) > 0, θ must be in the fourth quadrant, because cosine is positive in the first and fourth quadrants.

In the fourth quadrant, the reference angle for which tan(θ) = 1 is 45°. Therefore, the angle θ is 360° - 45°.

Calculate 360° - 45° to find the angle θ that satisfies both conditions.

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Identify what angle, θ\(\theta\)θ , satisfies the following conditions.tanθ=−1\(\tan\]\theta\)=-1tanθ=−1; cosθ\(\cos\]\theta\)cosθ > 000

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Identify what angle, $\theta$ , satisfies the following conditions.
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