Trigonometric Functions Summary

Radian Measures

• 360^\circ = 2\pi radians

Trigonometric Functions

• Functions: sin, cos, tan, csc, sec, cot
• Values for angles: \frac{\pi}{6}, \frac{\pi}{4}, \frac{\pi}{3}
• Pythagoras Theorem: a^2 + b^2 = c^2

Unit Circle

• A circle of radius 1 centered at (0,0).
• For any angle \theta, the y and x coordinates of the point P define the values of sin(\theta), and cos(\theta).

Tangent Function

• tan(\theta) = \frac{sin(\theta)}{cos(\theta)}
• The tangent function(tan) represents the slope of the line from the origin to the point P in the unit circle.

SOH CAH TOA

• sin(\theta) = \frac{Opposite}{Hypotenuse}
• cos(\theta) = \frac{Adjacent}{Hypotenuse}
• tan(\theta) = \frac{Opposite}{Adjacent}

Inverse Trig Functions

• sec(\theta) = \frac{1}{cos(\theta)} (secant)
• cosec(\theta) = \frac{1}{sin(\theta)} (cosecant)
• cot(\theta) = \frac{1}{tan(\theta)} = \frac{cos(\theta)}{sin(\theta)} (cotangent)

Graphs of Trig Functions

• Sine: y-value
• Cosine: x-value
• Tangent: slope

Periodicity

• Sine: sin(x + 2\pi) = sin(x), Range = [-1,1]
• Cosine: cos(x + 2\pi) = cos(x), Range = [-1,1]
• Tangent: tan(x + \pi) = tan(x), Range = R

Zeroes/Asymptotes

• Zeroes (sin) = {n\pi | n \in Z} = zeroes (tan)
• Zeroes (cos) = {\frac{\pi}{2} + n\pi, n \in Z} = asymptotes (tan)

Trig Identities

• cos^2(\theta) + sin^2(\theta) = 1
• 1 + tan^2(\theta) = sec^2(\theta)