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−90∘<θ<90∘-90^\circ < \theta < 90^\circ. Find the value of θ\theta in degrees.\newlinetan⁡(θ)=0\tan(\theta) = 0\newlineWrite your answer in simplified, rationalized form. Do not round.\newlineθ=\theta = ____∘^\circ\newline

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Inverses of sin, cos, and tan: degreesright chevron icon

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Q. −90∘<θ<90∘-90^\circ < \theta < 90^\circ. Find the value of θ\theta in degrees.\newlinetan⁡(θ)=0\tan(\theta) = 0\newlineWrite your answer in simplified, rationalized form. Do not round.\newlineθ=\theta = ____∘^\circ\newline
  1. Understand Tangent Ratio: We know that the tangent of an angle is the ratio of the sine to the cosine of that angle: tan⁡(θ)=sin⁡(θ)cos⁡(θ)\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}. For tan⁡(θ)\tan(\theta) to equal 00, the numerator of this fraction, sin⁡(θ)\sin(\theta), must be 00, because a fraction is only equal to zero when its numerator is zero. This is true as long as cos⁡(θ)\cos(\theta) is not also 00, because division by zero is undefined.
  2. Identify Angle with Sine 00: We need to find the angle θ\theta where the sine function is equal to 00 within the given interval −90∘<θ<90∘-90^\circ < \theta < 90^\circ. The sine function is equal to 00 at 0∘0^\circ and 180∘180^\circ, but since 180∘180^\circ is not within our interval, we can exclude it. Therefore, the only value for θ\theta that satisfies both conditions (sin⁡(θ)=0\sin(\theta) = 0 and −90∘<θ<90∘-90^\circ < \theta < 90^\circ) is 0000.

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