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STANDARDS

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US-VA

Math

Virginia Math

Trigonometry: Circular Trigonometry

T.CT.1

The student will determine the degree and radian measure of angles; sketch angles in standard position on a coordinate plane; and determine the sine, cosine, tangent, cosecant, secant, and cotangent of an angle, given a point on the terminal side of an angle in standard position or the value of a trigonometric function of the angle.

T.CT.1.a

Define a radian as a unit of angle measure and determine the relationship between the radian measure of an angle and the length of the intercepted arc in a circle.
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T.CT.1.b

Determine the degree and radian measure of angles to include both negative and positive rotations in the coordinate plane.
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T.CT.1.c

Find both positive and negative coterminal angles for a given angle.
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T.CT.1.d

Identify the quadrant or axis in/on which the terminal side of an angle lies.
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T.CT.1.e

Draw a reference right triangle when given a point on the terminal side of an angle in standard position.
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T.CT.1.f

Draw a reference right triangle when given the value of a trigonometric function of an angle (sine, cosine, tangent, cosecant, secant, and cotangent).
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T.CT.1.g

Determine the value of any trigonometric function (sine, cosine, tangent, cosecant, secant, and cotangent) when given a point on the terminal side of an angle in standard position.

T.CT.1.h

Given one trigonometric function value, determine the other five trigonometric function values.
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T.CT.1.i

Calculate the length of an arc of a circle in radians.
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T.CT.1.j

Calculate the area of a sector of a circle.
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T.CT.2

The student will develop and apply the properties of the unit circle in degrees and radians.

T.CT.2.a

Convert between radian and degree measure of special angles of the unit circle without the use of technology.
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T.CT.2.b

Define the six circular trigonometric functions of an angle in standard position on the unit circle.

T.CT.2.c

Apply knowledge of right triangle trigonometry, special right triangles, and the properties of the unit circle to determine trigonometric functions values of special angles (0°, 30°, 45°, 60°, and 90°) and their related angles in degree and radians without the use of technology.