Trigonometry in the Coordinate Plane PART TWO Trigonometry

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Trigonometry in the Coordinate Plane PART TWO

Trigonometry in the Coordinate Plane PART TWO

Trigonometry in Coordinate Plane

Trigonometry in Coordinate Plane

Trigonometry in Coordinate Plane

Trigonometry in Coordinate Plane

Trigonometry in Coordinate Plane

Trigonometry in Coordinate Plane

Trigonometry in Coordinate Plane Unit Circle We are now going back to this picture

Trigonometry in Coordinate Plane Unit Circle We are now going back to this picture and we are going to set the radius of the circle to 1 If r = 1 then sin θ = y/r becomes y/1 = y Similarly cos θ = x/r = x/1 = x So if the radius is 1 then we have the following relationships sin θ = y cos θ = x A circle where the radius is 1 is called a unit circle.

Trigonometry in Coordinate Plane So if I tell you the point (0. 283, 0.

Trigonometry in Coordinate Plane So if I tell you the point (0. 283, 0. 947) is on the unit circle then you already know the following: If I draw a line segment from the origin to the point (. 283, . 947) then the angle θ made from the x-axis to the line segment has a cos value of. 283 (x) and a sin value of. 947 (y)

Trigonometry in Coordinate Plane This brings us to another big idea! For any point

Trigonometry in Coordinate Plane This brings us to another big idea! For any point in the unit circle we can write it as (cos θ, sin θ) since cos θ = x and sin θ = y

Trigonometry in Coordinate Plane This means that we can find any point on the

Trigonometry in Coordinate Plane This means that we can find any point on the unit circle by finding the sine and cosine of the angle made from the origin to the line segment drawn from the origin to the point. For example, on the right we have the unit circle and the point on the unit circle. When we drew a line segment from the origin to that point it made an angle of 231 degrees. Using a calculator cos 231 = -0. 629 and sin 231 = -0. 777 So that point is (-0. 629, -0. 777)

Trigonometry in Coordinate Plane Because of our special triangles we already know three points

Trigonometry in Coordinate Plane Because of our special triangles we already know three points on the unit circle without using a calculator: (cos 30, sin 30) - the blue line (cos 45, sin 45) - the red line (cos 60, sin 60) - the black line

Trigonometry in Coordinate Plane

Trigonometry in Coordinate Plane

STOP IF YOU ARE UNSURE OF ANY OF THE IDEAS WE JUST COVERED IN

STOP IF YOU ARE UNSURE OF ANY OF THE IDEAS WE JUST COVERED IN THIS SECTION PLEASE TAKE SOME TIME TO REFLECT AND REREAD THIS SECTION AGAIN. WHEN YOU FEEL READY CONTINUE ON.