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A Great Tool to Use in Finding the Sine and Cosine of Certain Angles
UNIT CIRCLE A Great Tool to Use in Finding the Sine and Cosine of Certain Angles
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Start with the Coordinate Plane
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Draw a Circle whose center is at the origin
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Whose Radius is one unit
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1 Pick a point (x, y) on the circle and draw the terminal side of an angle through the point
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Because the Radius is one unit
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Every point (x, y) on the circle will have the coordinates
1 Every point (x, y) on the circle will have the coordinates
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Every point (x, y) on the circle will have the coordinates
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Every point (x, y) on the circle will have the coordinates
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Every point (x, y) on the circle will have the coordinates
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1 Which We Saw in the Past
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and
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1 Pythagoras
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1 Pythagoras
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1 Pythagoras
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1 Pythagoras
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1 Pythagoras
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1 Pythagoras
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1 Pythagoras
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1 Pythagoras
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1 Pythagoras
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The Big 2 1 Pythagoras
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Now
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Recall Radian Degree Circle
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Writing them INSIDE the circle
Degrees Writing them INSIDE the circle
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Writing them INSIDE the circle
Radians Writing them INSIDE the circle
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Next
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Put the Circle in the Coordinate Plane
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Let the Circle have a radius of 1
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What are the coordinates of
1 What are the coordinates of
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What are the coordinates of
1 What are the coordinates of
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What are the coordinates of
1 What are the coordinates of
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What are the coordinates of
1 What are the coordinates of
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Remember The Quadrantals
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If we made an ordered pair (cosine, sine) It would be (1,0) which were the coordinates of the point that the terminal side passes through when
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Same as it's Coordinates!
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If we made an ordered pair (cosine, sine) It would be (0,1) which were the coordinates of the point that the terminal side passes through when
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Same as it's Coordinates!
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If we made an ordered pair (cosine, sine) It would be (–1,0) which were the coordinates of the point that the terminal side passes through when
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Same as it's Coordinates!
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If we made an ordered pair (cosine, sine) It would be (0,–1 ) which were the coordinates of the point that the terminal side passes through when
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Same as it's Coordinates!
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They are the same as the Coordinates!
You Now Have An Easy Way To Remember The Cosine and Sine for the Quadrantal Angles They are the same as the Coordinates!
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Angles Whose Reference Angle is
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Writing them INSIDE the circle
Degrees Writing them INSIDE the circle
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Writing them INSIDE the circle
Radians Writing them INSIDE the circle
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From The Special Angles
Remember From The Special Angles
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We know that we can find the tangent, secant, cosecant and cotangent
Quadrant Angle I We know that we can find the tangent, secant, cosecant and cotangent When we know just the Cosine and Sine II III IV
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Quadrant Angle And we can determine if they are Positive or Negative in each Quadrant using the Table Below I II III IV
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Angles Whose Reference Angle is
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Writing them INSIDE the circle
Degrees Writing them INSIDE the circle
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Writing them INSIDE the circle
Radians Writing them INSIDE the circle
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From The Special Angles
Remember From The Special Angles
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We know that we can find the tangent, secant, cosecant and cotangent
Quadrant Angle I We know that we can find the tangent, secant, cosecant and cotangent When we know just the Cosine and Sine II III IV
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Quadrant Angle And we can determine if they are Positive or Negative in each Quadrant using the Table Below I II III IV
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Angles Whose Reference Angle is
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Writing them INSIDE the circle
Degrees Writing them INSIDE the circle
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Writing them INSIDE the circle
Radians Writing them INSIDE the circle
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From The Special Angles
Remember From The Special Angles
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We know that we can find the tangent, secant, cosecant and cotangent
Quadrant Angle I We know that we can find the tangent, secant, cosecant and cotangent When we know just the Cosine and Sine II III IV
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Quadrant Angle And we can determine if they are Positive or Negative in each Quadrant using the Table Below I II III IV
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Sine and Cosine of Angles
A Great Tool to Use in Finding the Sine and Cosine of Angles
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Remember that we can find the tangent, secant, cosecant and cotangent
When we know just the Cosine and Sine THE UNIT CIRCLE And now we have
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