TRIGONOMETRY
greek word “trigonon" (triangle) &
“metron" (measure)
studies the relationship between side lengths and angles of triangles
emerged during 3rd century BC An angle is:
Positive - ray rotates counterclockwise Negative - ray rotates clockwise
An angle is in standard position if its vertex is at ORIGIN and its initial side is on POSITIVE AXIS
RADIAN MEASURE
1 radian - measure of the central angle whose arc length is the same as the radius of the circle.
Radians to Degrees Degrees to Radian
Coterminal angles are angles in standard position that share the same terminal side.
- have the same reference angle Example:
DOMAIN AND RANGE OF THE SINE AND COSINE FUNCTIONS
o sin 𝑥 is defined for any real number x or the domain of the sine functions is ℝ.
o The range of sine is the set of all real numbers between -1 and 1 inclusive. Or [-1 to 1]
THE AMPLITUDE, PERIOD AND PHASE SHIFT OF THE GRAPHS OF CIRCULAR FUNCTIONS.
Amplitude of bounded periodic function is half the difference of the highest value and lowest value.
Period is the graph’s complete cycle.
Given 𝑦 = 𝑎 sin 𝑏𝜃 + 𝑐 + 𝑑 𝑎𝑛𝑑 𝑦 = 𝑎 cos 𝑏𝜃 + 𝑐 + 𝑑
amplitude = 𝑎 period = 2𝜋/b vertical shift = d horizontal shift = −𝑐/b
FUNDAMENTAL TRIGONOMETRIC IDENTITIES Identity- solution are set of real numbers & ALWAYS true Conditional- one or more solutions & SOMETIMES true Contradiction/ Inconsistent- has no solution & NEVER true
SUPER HEXAGON