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Exact Unit Circle Trigonometry worksheets

Practice radians, coterminal reduction, quadrants, reference angles, and exact sine, cosine, and tangent values.

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For each angle, identify its quadrant and reference angle, then give exact sin, cos, and tan values.

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Learning objective

What this activity builds

Use unit-circle coordinates and quadrant signs to evaluate exact trigonometric values.

Worked example

Evaluate the trig values at theta = 5pi/6.

Reference angle pi/6; sin=1/2, cos=-sqrt(3)/2, tan=-sqrt(3)/3.

The terminal side lies in quadrant II, so sine is positive while cosine and tangent are negative.

Teaching notes

Make the practice count

  • Reduce extended angles modulo 2pi first.
  • Write the unit-circle coordinate as (cos, sin).
  • Treat axis angles separately because tangent may be undefined.

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Math SheetNameScoreTeacherDateExact Unit Circle PracticeFor each angle, identify its quadrant and reference angle, then give exact sin, cos, and tan values.1.theta = 7pi/4: give the terminal-side location, reference angle when applicable, sin(theta), cos(theta), and tan(theta).2.theta = 5pi/3: give the terminal-side location, reference angle when applicable, sin(theta), cos(theta), and tan(theta).Show your reasoning. Keep exact values unless instructed otherwise.math-sheet.comPage 1 of 3
Math SheetNameScoreTeacherDateExact Unit Circle PracticeFor each angle, identify its quadrant and reference angle, then give exact sin, cos, and tan values.3.theta = 0: give the terminal-side location, reference angle when applicable, sin(theta), cos(theta), and tan(theta).4.theta = pi/6: give the terminal-side location, reference angle when applicable, sin(theta), cos(theta), and tan(theta).Show your reasoning. Keep exact values unless instructed otherwise.math-sheet.comPage 2 of 3
Math SheetNameScoreTeacherDateExact Unit Circle PracticeFor each angle, identify its quadrant and reference angle, then give exact sin, cos, and tan values.5.theta = 2pi/3: give the terminal-side location, reference angle when applicable, sin(theta), cos(theta), and tan(theta).6.theta = 5pi/6: give the terminal-side location, reference angle when applicable, sin(theta), cos(theta), and tan(theta).Show your reasoning. Keep exact values unless instructed otherwise.math-sheet.comPage 3 of 3

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