Module 10: Right Triangle Trigonometry and the Unit Circle

Theta

θ A variable typically used to represent a missing angle measure.

Unit Circle

A circle with a radius of 1, centered at the origin. Used to find the trigonometric ratios for angles.

SOH CAH TOA

A pneumonic device used to remember the trig ratios... SIN (Opposite/Hypotenuse) COS (Adjacent/Hypotenuse) TAN (Opposite/Adjacent)

Trigonometric Ratio

A ratio of the lengths of two sides in a right triangle.

Special Right Triangles (30-60-90)

A right triangle with the other two angles measuring 30° and 60°. Side Rations: 1-2-sqrt3

Special Right Triangles (45-45-90)

A right triangle with the other two angles measuring 45°. Side Ratios: 1-1-sqrt2

Right Triangle

A triangle that has a 90 degree angle.

Radian

A unit of angle measure, equal to an angle at the center of a circle whose arc is equal in length to the radius.

Angle in Standard Position

An angle with its initial side on the positive x-axis and its vertex at the origin.

Pythagorean Theorem

In a right triangle the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs A²+B²=C²

Secant (sec θ)

Reciprocal trig ratio for cosine 1/cosθ Hypotenuse/Adjacent

Cosecant (csc θ)

Reciprocal trig ratio for sine. 1/sinθ Hypotenuse/Opposite

Cotangent (cot θ)

Reciprocal trig ratio for tangent 1/tanθ Adjacent/Opposite

Initial Side of an Angle

Starting position of the rotated ray in the formation of an angle.

Reference Angle

The acute angle formed by the terminal side of an angle in standard position and the x-axis.

Trigonometry

The branch of mathematics dealing with the relations of the sides and angles of triangles and with the relevant functions of any angles. We are starting with Right Triangle Trigonometry - but there is much more to it than that!

Vertex

The common endpoint of an angle

Adjacent Leg

The leg (not the hypotentuse) of a right triangle that is next to the indicated angle (the endpoint of the leg is at the vertex of the angle).

Opposite Side

The leg (not the hypotenuse) of a right triangle that is across from the indicated angle (the side and the angle do not touch).

Cosine (cos θ)

The ratio of the adjacent side of a right triangle divided by the hypotenuse.

Tangent (tan θ)

The ratio of the side opposite of a right triangle divided by the adjacent side for a right triangle.

Sine (sin θ)

The ratio of the side opposite of a right triangle divided by the hypotenuse for a right triangle.

Terminal Side of an Angle

The ray where measurement of an angle stops

Hypotenuse

The side opposite the right angle in a right triangle. This will always be the longest side of the triangle (since it is across from the largest angle).

Coterminal Angles

Two angles in standard position that have the same terminal side.

Converting Radians to Degrees

multiply by 180/π

Converting Degrees to Radians

multiply by π/180