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Basic Trig Dr. Robert MacKay Clark College Physics

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Introduction Right angle trig Sine, cosine, tangent Pathagorean Theorm Inverse tangent

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Basic Definitions For a right triangle (90°) y r x y x Sin = y r Cos = x r Tan = r 2 = x 2 + y 2 = ATAN (y / x)

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Y=? V=10m/s X=? =40°

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Y=6.4 m/s V=10m/s X=7.7 m/s =40° Sin = Y V Y= VSin 40° = 10m/s(0.643) = 6.43 m/s Cos = V X= VCos 40° = 10m/s(0.766) = 7.66 m/s X

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Basic Definitions Y=? V=?m/s X=20 m/s =40° y x Sin = y V Cos = x V tan = 1.25.2 m/s 2.25.9 m/s 3.26.1 m/s 4.26.8 m/s

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Y=? V=?m/s X=20 m/s =37° Y X Cos = x V tan = V Cos =x Cos x V = = Cos 20m/s = 26.1 m/s Y=X tan =20 m/s (.84) =16.8 m/s

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a=? R=? 70° 8m 1.8.6 2.8.6 3.8.1 4.8.5 5.8.4 a= 1.2.9 2.3.2 3.2.8 4.2.8 5.2.7

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a=? R=20 8m Sin = 8 20 Cos = a V =.4 =sin -1 (.4)=23.6°

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Basic Definitions For a right triangle (90°) y r x x r Sin = y r Cos = x r tan =

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Basic Definitions For a right triangle (90°) y r x x r Sin = y r Cos = x r tan =

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Basic Definitions For a right triangle (90°) y r x x r Sin = y r Cos = x r tan =

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Vector addition Vector addition. The method of adding two vectors to give their resultant effect. R=A + B A B

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Vector Components Vector components - 2 mutually perpendicular vectors which when added give the original vector A=Ax+Ay A Ax Ay

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Vector Componts East North for a 45° Nof E Ax=10 Ay=10 A=?

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Vector Componts What are the North and east components for a velocity 45° N of E Ax=? Ay=? A=141 m/s

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Vectors A and B are at right angles. A has a magnitude of 20 m/s and B has a magnitude of 10 m/s. Find the magnitude of the resultant vector A+B. For the vectors A and B in the figure above calculate the direction (in degrees) that the resultant vector A+B makes with the x-axis (A direction).

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Vectors A and B have magnitudes of 18 N and 8 N respectively. They are oriented 45 degrees from each other as shown. What is the magnitude of the resultant vector A+B?

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Independence of Vector Components For 2-D projectile motion the vertical and horizontal motions are independent Vx=10 m/s Vy=10 m/s V

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For 2-D projectile motion the vertical and horizontal motions are independent

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Independence of Vector Components 2-14 A small plane takes off with a constant velocity of 150 km/hr (42 m/s) at an angle of 37 °. In 3.00 s, A) how high is the plane above the ground? B) What horizontal distance has it traveled?

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Independence of Vector Components 2-13** A ball has an initial velocity of 1.3 m/s along the +y direction and starting at t o receives an acceleration of 2.10 m/s 2 in the +x direction. A) what is the position of the ball at 2.5 sec after t o ? B) What is the velocity of the ball at that time?

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