Trigonometry

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Trigonometry

  1. 1. TRIGONOMETRY UNITS 1 &2By Leslie Zamudio
  2. 2. HOW TO MEASURE IN BOTH DEGREES &RADIANS An angle is an opening of a circle measuredin degrees & a radian is a measurementthat is equal to the length of the radiuswhich is the same as the arc length. Everyangle is equal to a radian. Multiplying anyradian by 180/∏
  3. 3. SINE AND COSINE Sine and cosine are the x and y values of the unitcircle Every angle, radian or degree has a corresponding(x,y) coordinate on the unit circle
  4. 4. SINE AND COSINE The sine graph begins at the origin, the cosinegraph begins at 1
  5. 5. SOLVING FOR SINE AND COSINE Solving for sine and cosine, you need and angleand the hypotenuse Plugging in what you know, can solve for othersides and angles. Using the Pythagorean theorem and the Law ofCosines and the Law of Sines, inverse cosine andinverse sine may also help
  6. 6. UNIT 2 F(x)= a sin (bx+c)+d F(x)= a cos (bx+c)+d The frequency of the graphs is the number ofwaves per minute The period is the duration of a wave The amplitude is the height (y-axis) a wave goes
  7. 7. UNIT 2 A phase shift refers to a horizontal or verticaltranslation according to the equation. The phaseshift is defined by c (F(x)= a sin (bx+c)+d ) . If c isnegative the graph shifts over to the right, if it ispositve it shifts to the left. The image below shows the shift of a cosine graphstarting from one to zero, also the period of eachwave decreases creating moreWaves within one period.
  8. 8. UNIT 2 Inverse sin-1 / arcsine Inverse cos-1 / arccosine Inverse tan-1 / arctangent The inverse and the arc finds the measurement ofthe angle Example :cos150° 150° is equal to 5/6giving the angle a coordinateof (-√3/2, ½) Cosine is equal to x , sineis equal to y Therefore, cos150° is -√3/2

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