Unit Circle Fill in Worksheet

The unit circle fill in worksheet is an essential tool for students studying trigonometry or preparing for the SAT Math subject test. Designed to help learners understand the interconnectedness of angles, radians, and trigonometric functions, this worksheet provides a hands-on approach to mastering the unit circle.

  Blank Unit Circle with Degrees

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  Unit Circle with Tangent Chart

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  Blank Unit Circle with Tangent

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  Blank Unit Circle

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  Blank Unit Circle Worksheet

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  Unit Circle Blank Template

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  Printable Blank Unit Circle

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  Printable Blank Unit Circle

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  Unit Circle Practice Sheet

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  Blank Unit Circle Quiz

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  Blank Unit Circle

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What is the radius of the unit circle?

The radius of the unit circle is 1 unit.

What are the coordinates of the point on the unit circle that corresponds to a 30-degree angle?

The coordinates of the point on the unit circle that corresponds to a 30-degree angle are (√3/2, 1/2).

At what angle does the sine value reach its maximum on the unit circle?

The sine value reaches its maximum at an angle of 90 degrees (or π/2 radians) on the unit circle. This is where the y-coordinate of a point on the unit circle is at its highest point, which corresponds to a sine value of 1.

What is the cosine value at a 45-degree angle?

The cosine value at a 45-degree angle is 0.70710678118, or approximately 0.71.

What is the tangent value at a 60-degree angle?

The tangent value at a 60-degree angle is √3, which is approximately 1.73205.

What is the angle measure at the point (-1/2, √3/2) on the unit circle?

The angle measure at the point (-1/2, √3/2) on the unit circle is 120 degrees (or 2π/3 radians) as this point corresponds to the angle of 120 degrees in standard position, or 2π/3 radians, when measured counterclockwise from the positive x-axis on the unit circle.

What is the angle measure at the point (1/2, -√3/2) on the unit circle?

The angle measure at the point (1/2, -√3/2) on the unit circle is 300 degrees or 5π/6 radians. This point corresponds to the third quadrant of the unit circle where the cosine is 1/2 and the sine is -√3/2.

What is the value of the sine function at a 180-degree angle?

The value of the sine function at a 180-degree angle is 0.

At what angle does the cosine function have a negative value on the unit circle?

The cosine function has a negative value on the unit circle at angles between 90 degrees and 270 degrees, or in radians between π/2 and 3π/2.

What is the tangent of a 90-degree angle on the unit circle?

The tangent of a 90-degree angle on the unit circle is undefined, as at that angle the cosine is 0, and division by zero is undefined.