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WAC TYPE 2: WAC TYPE 2: WHAT IS THE RELATIONSHIP BETWEEN THE SINE AND COSINE FUNCTIONS OF THE ACUTE ANGLES IN A RIGHT TRIANGLE? http://padlet.com/wall/8tx4w84jl8sl

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IN CASE YOU MISSED IT

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THE UNIT CIRCLE

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WHAT IS A UNIT CIRCLE?

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THE UNIT CIRCLE If this is a circle with radius = 1, label the coordinates of the points where the circle crosses the x and y axes. Can we label the coordinates of the other points along the unit circle where the major angles are? Take out your unit circle from the page protector and fill in the coordinates according to the activity we just did.

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TRIG AND THE UNIT CIRCLE Go back in your notes to our table of trig values for the major angles. Compare these values to the coordinates we just found. What do you notice?! The x-coordinate is sin θ and the y-coordinate is cos θ!!! An (x,y) ordered pair on the unit circle gives you the sin and cos values, which will allow you to find other trig function values…THIS IS HUGE!!

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REFERENCE ANGLES Let Ө be an angle in standard position. Its reference angle is the acute angle, Ө’, formed by the terminal side of Ө and the horizontal axis The trig function’s value for Ө is the same as the associated reference angle, Ө’, the only thing that is different is the sign TO FIND REFERENCE ANGLES: Quadrant 2:Quadrant 3:Quadrant 4: When working in radians, the reference angles are the ones with the same denominator

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REDEFINING THE TRIG FUNCTIONS IN THE UNIT CIRCLE Now that we know how the trig functions relate to the coordinates on the unit circle, we are going to redefine how we find them.

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REDEFINING THE TRIG FUNCTIONS IN THE UNIT CIRCLE Now that we know how the trig functions relate to the coordinates on the unit circle, we are going to redefine how we find them.

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A LL S TUDENTS T AKE C ALCULUS Since sine is the y coordinate, it will be positive in the first and second quadrants. Since cosine is the x coordinate, it will be positive in the first and fourth quadrants. What about tangent? Or, just remember All Students Take Calculus All trig functions are positive in Q1 Sine (and cosecant) are positive in Q2 Tangent (and cotangent) are positive in Q3 Cosine (and secant) are positive in Q4

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THE LEFT HAND TRICK Imagine your left hand as an axis showing the first quadrant. Your thumb is the y-axis and your pinky is the x-axis. Imagine the other fingers are our important angles. To find the sine value, hold down the finger that represents the angle you want. Now count the number of fingers below the bent one. This goes under the radical. To find the cosine value, do the same as above, but count the fingers above the bent one. To find the tangent value, take the square root of the bottom fingers over the square root of the top ones (ignore the 2).

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1 1 - 1 Every ray that comes from the origin and intersects the unit circle has a length of 1 (because it is a radius) r =1 A right triangle can be created.

1 1 - 1 Every ray that comes from the origin and intersects the unit circle has a length of 1 (because it is a radius) r =1 A right triangle can be created.

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