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Unit 8 (SohCahToa (sin theta=y/r, cos theta=x/r, tan theta=y/x, 30,60,90…
Unit 8
SohCahToa
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30,60,90 triangles have the sides x, x root 3, 2x
45,45,90 triangles have the sides x, x, x root 2
Rectangular Vectors
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when adding the coordinates just add x's and y's same with subtraction, multiplication, and division
When adding on the graph, graph the vectors singularly first then find the resultant angle by connecting the starting point to the end point.
Polar Coordinates
( r, theta ): r is the distance from the origin and theta is the rotation up and down in degrees
When graphing rings of circle is the r and the rotation is still theta marked with the straight lines at each 15 degree interval
Converting to rectangular use a diagram and Pythagorean theorem to get the value of r and then use inverse tangent to get the theta or the reference angle then doing 180-the reference angle to get theta
Reference Angles
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depending on which quadrant the given angle is in the answer should match with the negative or positives of original angle.
Sin is positive in the first and second quad. Cos is positive in first and forth quads and Tan is positive in first and third quads.
Polar Vectors
Use ruler and protractor to graph the vectors, otherwise just add the r's and thetas like rectangular vectors for the resultant vector
when adding them without vectors need to convert coordinate to rectangular then back to polar to get the resultant answer
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