Trigonometric Functions

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Move the point labeled "Move" to adjust the angle between the ray and the x-axis.

If Hypoteneuse = r = 1 (a unit circle), then:

Opposite = sin(θ) = y

Adjacent = cos(θ) = x

SOHCAHTOA:

SOH: Opposite / Hypoteneuse = sin(θ) = y / r

CAH: Adjacent / Hypoteneuse = cos(θ) = x / r

TOA: Opposite / Adjacent = tan(θ) = y / x

Other Functions:

Hypoteneuse / Opposite = csc(θ) = r / y = 1 / sin(θ)

Hypoteneuse / Adjacent = sec(θ) = r / x = 1 / cos(θ)

Adjacent / Opposite = cot(θ) = x / y = 1 / tan(θ)

1 = csc(θ)^2 - cot(θ)^2

1 = sec(θ)^2 - tan(θ)^2

1 = sin(θ)^2 + cos(θ)^2

1 = sec(θ) - exsec(θ)

1 = csc(θ) - coexsec(θ)

1 = vers(θ) + cos(θ)

1 = sin(θ) + covers(θ)

hav(θ) = vers(θ) / 2

Pythagorean Theorem:

c^2 = a^2 + b^2

where Adjacent = a, Opposite = b, and Hypoteneuse = c.

Law of Sines:

2 * r = a / sin(A) = b / sin(B) = c / sin(C)

where "r" is the radius of the circumcircle,

and a = Adjacent, b = Opposite, and c = Hypoteneuse,

and A = the angle opposite a, B = the angle opposite b, and C = the angle opposite c.

Law of Cosines:

cos(A) = (c^2 + b^2 - a^2) / (2 * b * c)

where a = Adjacent, b = Opposite, and c = Hypoteneuse,

and A = the angle opposite a.

Law of Tangents:

(a + b) / (a - b) = tan((A + B) / 2) / tan((A - B) / 2)

where a = Adjacent, b = Opposite, and c = Hypoteneuse,

and A = the angle opposite a, and B = the angle opposite b.

Dot Product:

A•B = cos(θ) = x_A * x_B + y_A * y_B

where A and B are vectors with lengths equal to 1.

Download the worksheet. Note: the file is not a Zip file, even though it has the "zip" extension. Simply change the extension to "ggb" after downloading it. You can download an old Geometer's Sketchpad version of this worksheet, here.

Created by Michael Horvath using GeoGebra. Last modified: Monday, 08-Dec-08 13:27:16 PST

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