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Unit circle and obtuse angles
This test uses the unit circle to determine trigonometric values. Tasks cover quadrants, signs of sine and cosine, obtuse and supplementary angles and checking whether a resulting value is reasonable.
Questions: 10Estimated time: 14 minutes
Time left: 00:00:00
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Top 10 registered students. Only each student’s best result in the period counts.
Sample questions
- Give the unit-circle point coordinates for angle ___°.
- Simplify sin(180° − ___°).
- Simplify cos(180° − ___°).
- Simplify tan(180° − ___°).
- An acute angle α has sine ___. What is sin(180° − α)?
Unit circle and obtuse angles
On the unit circle, the point corresponding to angle α has coordinates (cos α, sin α). Thus sine is the y-coordinate, cosine the x-coordinate, and tan α = sin α / cos α whenever cos α ≠ 0.
Signs and reference angles
In quadrant II, sine is positive while cosine and tangent are negative. Reference angles give values such as sin(180° − α) = sin α and cos(180° − α) = −cos α. Determine the quadrant before choosing a sign.
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