Unit 7 - Trigonometry Terms
Pi (π)
A ratio that compares the circumference of a circle divided by its diameter.
Degree
A unit of measure for angles. 1 degree is equal to 1/360 of a full rotation.
Pythagorean triple
A set of three whole numbers that work with the Pythagorean theorem (e.g., 3-4-5, 5-12-13, 8-15-17)
Right Triangle
A triangle with one 90° angle. The other two angles are acute (and complementary).
Adjacent
The side next to the reference (θ) angle.
Converse of the Pythagorean theorem
Used to determine whether certain lengths represent sides of a right triangle.
Obtuse triangle
When the square of the longest side is GREATER than the sum of the squares of the shorter sides
Acute triangle
When the square of the longest side is SHORTER than the sum of the squares of the shorter sides
Straight angle
θ = 180 degrees or π radians
A half rotation around the unit circle
π radians or 180°
A quarter rotation around the unit circle
π/2 radians or 90°
Acute angle
0 < θ < 90 degrees or 0 < θ < π/2 (radians)
A full rotation around the unit circle
2π radians or 360°
A 3/4 rotation around the unit circle
3π/2 radians or 270°
Obtuse angle
90 < θ < 180 degrees or π/2 < θ < π radians
Unit Circle
A circle with a radius of 1, centered at the origin
Angle
A figure formed by two rays with a common endpoint.
Trigonometric Ratio
A ratio of the lengths of two sides in a right triangle.
Radian
A unit of measure for angles. It is a ratio that compares the arc length of a circle to its radius. When the arc length is equal to the radius you have exactly 1 radian.
Right Angle
An angle of 90 (degrees) or θ = π/2 (radians)
Angle of depression
Angle formed by a hypotenuse drawn below the horizontal
Angle of elevation
Angle formed by a hypotenuse elevated above the horizontal
Pythagorean theorem
In a right triangle the square of the hypotenuse length is equal to the sum of the squares of the leg lengths A²+B²=C².
Arccosine (cos⁻¹)
Inverse to cosine. The angle found by comparing the adjacent side over the hypotenuse of a right triangle.
Arcsine (sin⁻¹)
Inverse to sine. The angle found by comparing the opposite side over the hypotenuse of a right triangle.
Arctangent (tan⁻¹)
Inverse to tangent. The angle found by comparing the opposite side over the adjacent side of a right triangle.
Theta
Letter of the Greek alphabet often used as a variable to represent angle measure.
One rotation around the unit circle
Measures 2 pi radians because the radius is 1 so the circumference is 2 pi r
Converting Radians to Degrees
Multiply by 180/π
Converting Degrees to Radians
Multiply by π/180
45,45,90 triangle
One of the two special right triangles (isosceles).
30,60,90 triangle
One of the two special right triangles.
Special Right Triangles
Refers to the 45-45-90 and 30-60-90 right triangles. Isosceles right triangle (45°, 45°, 90°). Right triangle whose short leg is exactly half the length of the hypotenuse (30°, 60°, 90°).
Trigonometry
The branch of mathematics that deals with the relations between the sides and angles of plane or spherical triangles, and the calculations based on them.
Vertex
The common endpoint of an angle
Adjacent leg
The leg that forms the reference (θ) angle of a right triangle with the hypotenuse.
Opposite Leg
The leg that is across from the reference angle (θ) of a right triangle. It is not part of the angle.
Cosine (cos)
The ratio of the adjacent leg over the hypotenuse of a right triangle.
Tangent
The ratio of the side opposite of a right triangle divided by the adjacent side for a right triangle.
Sine (sin)
The ratio of the side opposite of a right triangle divided by the hypotenuse for a right triangle.
Hypotenuse
The side opposite the right angle in a right triangle. Also the longest side of a right triangle.
A variable typically used to represent a missing angle measure.
Theta - θ
Supplementary angles
Two angles whose sum is 180° (π radians).
Complementary angles
Two angles whose sum is 90° (π/2 radians).