9.2 Exact trigonometric values

Ideas in this lesson

Sine and cosine

On the unit circle, cosine is the horizontal coordinate and sine is the vertical coordinate.

Exact cosine values

Use the horizontal coordinate of the unit-circle point and the angle’s quadrant.

Tangent and reciprocals

Tangent is sine divided by cosine where cosine is nonzero; reciprocal functions require nonzero denominators.

Signs and quadrants

Use the quadrant to determine signs before selecting a square root from a Pythagorean identity.

Pythagorean relationships

For a right triangle, the hypotenuse is opposite the right angle and the two legs satisfy the Pythagorean theorem.