–90° < θ < 90°. Find the value of θ in degrees. tan(θ) = 0 Write your answer in simplified, rationalized form. Do not round. θ = ____°

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). For tan(θ) to equal 0, the numerator of this fraction, sin(θ), must be 0, because a fraction is only equal to zero when its numerator is zero. This is true as long as cos(θ) is not also 0, because division by zero is undefined.Identify Angle with Sine 0: We need to find the angle θ where the sine function is equal to 0 within the given interval -90° < θ < 90°. The sine function is equal to 0 at 0° and 180°, but since 180° is not within our interval, we can exclude it. Therefore, the only value for θ that satisfies both conditions (sin(θ) = 0 and -90° < θ < 90°) is θ = 0°.

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-90^\circ < \theta < 90^\circ. Find the value of $\theta$ in degrees. $\newline$ $\tan(\theta) = 0$ $\newline$ Write your answer in simplified, rationalized form. Do not round. $\newline$ $\theta =$ ____ $^\circ$ $\newline$

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Math Problems

Algebra 2

Inverses of sin, cos, and tan: degrees

Full solution

-90^\circ < \theta < 90^\circ

. Find the value of

\theta

in degrees.

\newline

\tan(\theta) = 0

\newline

Write your answer in simplified, rationalized form. Do not round.

\newline

\theta =

____

^\circ

\newline

Understand Tangent Ratio: We know that the tangent of an angle is the ratio of the sine to the cosine of that angle: $\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}$ . For $\tan(\theta)$ to equal $0$ , the numerator of this fraction, $\sin(\theta)$ , must be $0$ , because a fraction is only equal to zero when its numerator is zero. This is true as long as $\cos(\theta)$ is not also $0$ , because division by zero is undefined.
Identify Angle with Sine $0$ : We need to find the angle $\theta$ where the sine function is equal to $0$ within the given interval -90^\circ < \theta < 90^\circ. The sine function is equal to $0$ at $0^\circ$ and $180^\circ$ , but since $180^\circ$ is not within our interval, we can exclude it. Therefore, the only value for $\theta$ that satisfies both conditions ( $\sin(\theta) = 0$ and -90^\circ < \theta < 90^\circ) is $0$ $0$ .