Trigonometry 1

Straight Angle

θ = π (radians)

Right Angle

θ = π/2 (radians)

Obtuse Angle

π/2 < θ < π (radians)

Special Right Triangles

(45°, 45°, 90°) Isosceles right triangle. (30°, 60°, 90°) Right triangle whose short leg is exactly half the length of the hypotenuse.

Acute Angle

0 < θ < π/2 (radians)

Inverse Function

A function whose domain (input) has been switched with its range (output).

Radian

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 of these.

Pi (π)

A ratio that compares the circumference of a circle divided by its diameter.

Trigonometric Ratio

A ratio that compares two sides of a right triangle for a given angle.

Right Trianlge

A triangle with one angle that is 90°. The other two angles are acute.

Degree

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

Coterminal Angles

Angles in standard position that have a common terminal side. We find them by adding or subtracting revolutions (360⁰ or 2π).

Clockwise

In standard position, negative angles are measured in a _______________ direction.

Counter Clockwise (Anti-Clockwise)

In standard position, positive angles are measured in _______________________ direction.

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.

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.

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.

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. x

Sine (sin)

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

Trigonometry

The study of the relationships between the sides and angles of triangles.

Supplementary Angles

Two angles whose sum is 180° (π radians).

Complementary Angles

Two angles whose sum is 90° (π/2 radians).

Reciprocals

Two values whose product is one.