Unit 9 Mastery Check

Give one positive and one negative angle coterminal with $310$ degrees.

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Give one positive and one negative angle coterminal with $310$ degrees.

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State the defining idea behind directed rotation and coterminal angles in one precise sentence.

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For directed rotation and coterminal angles, what condition or domain restriction must remain visible in the solution?

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Convert $73.625$ degrees to degrees, minutes, and seconds.

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Convert $73.625$ degrees to degrees, minutes, and seconds.

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State the defining idea behind degree measure and angular coordinates in one precise sentence.

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For degree measure and angular coordinates, what condition or domain restriction must remain visible in the solution?

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An arc of length $8.4$ lies on a circle of radius $3.5$. Find the angle in radians.

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An arc of length $8.4$ lies on a circle of radius $3.5$. Find the angle in radians.

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State the defining idea behind radian measure as normalized arc length in one precise sentence.

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For radian measure as normalized arc length, what condition or domain restriction must remain visible in the solution?

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A sector has area $54$ square centimeters and radius $6$ centimeters. Find theta.

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A sector has area $54$ square centimeters and radius $6$ centimeters. Find theta.

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State the defining idea behind arc length and sector area in one precise sentence.

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For arc length and sector area, what condition or domain restriction must remain visible in the solution?

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A point $0.8$ meter from an axis moves at $\frac{5 m}{s}$. Find angular speed.

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A point $0.8$ meter from an axis moves at $\frac{5 m}{s}$. Find angular speed.

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State the defining idea behind angular speed and linear speed in one precise sentence.

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For angular speed and linear speed, what condition or domain restriction must remain visible in the solution?

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Which unit-circle point corresponds to $t=-\frac{pi}{3}$?

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Which unit-circle point corresponds to $t=-\frac{pi}{3}$?

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State the defining idea behind wrapping the real line around the unit circle in one precise sentence.

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For wrapping the real line around the unit circle, what condition or domain restriction must remain visible in the solution?

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If sin $t=-\frac{4}{5}$ and cos $t>0,$ find cos $t$ and the quadrant.

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If sin $t=-\frac{4}{5}$ and cos $t>0,$ find cos $t$ and the quadrant.

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State the defining idea behind sine and cosine as coordinate functions in one precise sentence.

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For sine and cosine as coordinate functions, what condition or domain restriction must remain visible in the solution?

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Find$$sin(\frac{3pi}{4}) \qquad cos(\frac{3pi}{4})$$

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Find$$sin(\frac{3pi}{4}) \qquad cos(\frac{3pi}{4})$$

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State the defining idea behind exact values from special triangles in one precise sentence.

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For exact values from special triangles, what condition or domain restriction must remain visible in the solution?

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Evaluate $cos(-\frac{5pi}{4})$ exactly.

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Evaluate $cos(-\frac{5pi}{4})$ exactly.

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State the defining idea behind reference angles, quadrants, and signs in one precise sentence.

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For reference angles, quadrants, and signs, what condition or domain restriction must remain visible in the solution?

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