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Unit Circle values

The sixties (60,120,240,300)

The thirties (30,150,210,330)

The angles that form a 60 degree angle to the x axis all have the same values for the x and y coordinates. The origin is at the center of the circle,so moving left from the center will give a positive x coordinate, right a negative x coordinate, up a positive y coordinate and down a negative y coordinate. The angles that form a 30 degree angle to the x axis all have the same values for the x and y coordinates. The origin is at the center of the circle,so moving left from the center will give a positive x coordinate, right a negative x coordinate, up a positive y coordinate and down a negative y coordinate.
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The fortyfives (45,135,225,315)

The nineties and zeros (0,90,180,270)

The angles that form a 45 degree angle to the x axis all have the same values for the x and y coordinates. The origin is at the center of the circle,so moving left from the center will give a positive x coordinate, right a negative x coordinate, up a positive y coordinate and down a negative y coordinate. The angles that form a 0 or 90 degree angle to the x axis have a zero, one or negative one for their coordinates. The origin is at the center of the circle,so moving left from the center will give a x coordinate of -1 and y zero, right a x coordinate of 1 and y zero, up y coordinate of 1 and x 0, and down y coordinate of -1 and x 0.
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Trig Values: sine and cosecant, cosine and secant, tangent and cotangent

Sine and Cosecant

Sine Value: The sine value is the y coordinate on the unit circle.The y coordinate is the second coordinate in the pair. Cosecant Value: Flip the sine value over. When that puts a square root in the denominator, you need to move the square root to the numerator and leave a copy of the number behind in the denominator.
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Cosine and Secant

Cosine Value : The cosine value is the x coordinate on the unit circle.The x coordinate is the first coordinate in the pair. Secant value: Flip the cosine value over. When that puts a square root in the denominator, you need to move the square root to the numerator and leave a copy of the number behind in the denominator.
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Tangent and cotangent

The tangent value is the y coordinate divided by the x coordinate. If you end up with a stacked fraction, unstack it by mutliplying by the reciprocal. Review divide fractions on fraction page for help with that. The cotangent value is the x coordinate divided by the y coordinate.If you end up with a stacked fraction, unstack it by mutliplying by the reciprocal. Or, if you have the tangent value, flip it over.
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Practice!

Special Angles:

Special Angles - Degrees Matching | Moving Special Angles - click graph to match angle | Time Trial: Special Angles - click on dot

Reference Angles:

Reference Angles -Matching

Sine and Cosine Values:

Bowl for sine values | Bowl for cosine values | Mixed Sine and Cosine | Where's the Other Angle?
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cool math memorizing unit circle