Trigonometric Function Precalculus PREC111 PDF
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Mandaluyong College of Science and Technology
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These notes from Mandaluyong College of Science and Technology cover trigonometric functions in precalculus. The document outlines concepts like standard equations of circles, the unit circle, and the point function. It also explores circular functions and their properties, along with examples.
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MECHNOLOGYC ANDALUYONG S OLLEGE OF T CIENCE & TRIGONOMETRIC FUNCTION Precalculus PREC111 MECHNOLOGYC ANDALUYONG OLLEGE OFS T CIENCE & Recall: Standard equat...
MECHNOLOGYC ANDALUYONG S OLLEGE OF T CIENCE & TRIGONOMETRIC FUNCTION Precalculus PREC111 MECHNOLOGYC ANDALUYONG OLLEGE OFS T CIENCE & Recall: Standard equation of a circle with radius and center (h,k):. Unit Circle: A circle with (h,k) = (0,0) and r = 1 Circumference: MECHNOLOGYC ANDALUYONG OLLEGE OFS T CIENCE & THE POINT FUNCTION The point function P is a function that sends a real number to a point P() = (xy) on the unit ℝxℝ circle. P: P() = (x,y) How does P send to P() MECHNOLOGYC ANDALUYONG S OLLEGE OF T CIENCE & MECHNOLOGYC ANDALUYONG S OLLEGE OF T CIENCE & P(is the point on the unit circle making an arclength of from the point (1,0), measured counterclockwise if , and clockwise if. MECHNOLOGYC ANDALUYONG S OLLEGE OF T CIENCE & Examples: 1. P(0) = (1, 0) 6. P(-) = 2. P(= 7. P(-= 3. P() = 8. P(-) = 4. P() = 9. P(-) = 5. P() = MECHNOLOGYC ANDALUYONG S OLLEGE OF T CIENCE & THE POINT FUNCTION AND CIRCULAR FUNCTIONS ℝxℝ is a function that sends a ℝ Recall: The point function P: to a point P() = (x,y) on the unit circle 1. MECHNOLOGYC ANDALUYONG OLLEGE OFS T CIENCE & THE POINT FUNCTION AND CIRCULAR FUNCTIONS Let ℝ and P() = (x , y) we define the ff: x:=cos y: = sin We also write P() = (cos , sin) Example: P(0) = (1,0) cos = 1 sin = 0 MECHNOLOGYC ANDALUYONG S OLLEGE OF T CIENCE & THE POINT FUNCTION AND CIRCULAR FUNCTIONS Example: P() = (0,1) cos = 0 sin = 1 Domain P = all real numbers Range P = {(x,y)/=1} MECHNOLOGYC ANDALUYONG S OLLEGE OF T CIENCE & THE POINT FUNCTION AND CIRCULAR FUNCTIONS Some properties of P(). Let ℝ. P(, kZ 1. P()= P() P(k)= P() cos()= cos sin()= sin cos(k)= cos sin()= sin MECHNOLOGYC ANDALUYONG OLLEGE OFS T CIENCE & THE POINT FUNCTION AND Some properties of P(). Let ℝ. P(, kZ CIRCULAR FUNCTIONS 2. + = 1 3. P() = (cos , sin ) Q1 (+,+) Q2 ( -, +) Q3 (-, -) Q4 (+, -) MECHNOLOGYC ANDALUYONG S OLLEGE OF T CIENCE & Example: Which quadrant does P() lie? 1. P( 2. P() 3. P(-4) MECHNOLOGYC ANDALUYONG S OLLEGE OF T CIENCE & Example: Given sin and P() is in quadrant 2. what is cos ?
