4.3 Right Triangle Trigonometry - Day 1 Notes

Obtuse Angle

90° < θ < 180° π/2 < θ < π (radians)

Straight Angle

θ = 180° θ = π (radians)

Right Angle

θ = 90° θ = π/2 (radians)

Acute Angle

0° < θ < 90° 0 < θ < π/2 (radians)

Unit Circle

A circle at the origin with a radius of exactly 1 unit.

Radian

A unit of measure for angles based on the radius of the circle. When the arc length is equal to the radius you have 1 radian.

Degree

A unit of measure for angles. 1 degree is equal to 1/360 of a full rotation.

Trigonometric Ratio

Compares two sides of a right triangle for a given angle.

Pythagorean Theorem

For a right triangle with legs "a" and "b", and hypotenuse "c", a² + b² = c².

30-60-90 Triangle Theorem

In a 30°-60°-90° triangle, the length of the hypotenuse is twice the length of the shorter leg and the longer leg is √3 time the length of the shorter leg.

45-45-90 Triangle Theorem

In a 45°-45°-90° triangle, both legs are congruent and the length of the hypotenuse is √2 times the length of a leg.

Clockwise

In standard position negative angles are measured in this direction.

Counter Clockwise

In standard position positive angles are measured in this direction.

Secant (sec)

Reciprocal to cosine. The ratio of the hypotenuse over the adjacent leg of a right triangle.

Cosecant (csc)

Reciprocal to sine. The ratio of the hypotenuse over the opposite leg of a right triangle.

Cotangent (cot)

Reciprocal to tangent. The ratio of the adjacent side over the opposite side of a right triangle.

Hypotenuse

The longest side of a right triangle.

Cosine (cos)

The ratio of the adjacent leg over the hypotenuse of a right triangle.

Tangent (tan)

The ratio of the opposite leg over the adjacent leg of a right triangle.

Sine (sin)

The ratio of the opposite leg over the hypotenuse of a right triangle.

angle of depression

angle formed from a horizontal line down to a given diagonal

angle of elevation

angle formed from a horizontal line up to a given diagonal