Basic Trig Dr. Robert MacKay Clark College Physics

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

Basic Definitions y r Sin q= y r x Cos q= q r x y Tan q= x For a right triangle (90°) y r Sin q= y r x Cos q= q r x y Tan q= x r2 = x2 + y2 q =ATAN (y / x)

V=10m/s Y=? q=40° X=?

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

Basic Definitions y V=?m/s Sin q= V Y=? x Cos q= q=40° V X=20 m/s y tan q= x

x Cos q= V Cos q=x V 20m/s x = = 26.1 m/s V = Cos q Cos 40° V=?m/s Y=? Y tan q= X q=37° Y=X tan 40° =20 m/s (.84) =16.8 m/s X=20 m/s

a=? a= 2.9 3.2 2.8 2.7 70° 8m R=? 8.6 8.1 8.5 8.4

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

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

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

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

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

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

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

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

Vectors A and B are at right angles 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).

Vectors A and B have magnitudes of 18 N and 8 N respectively 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?

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

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

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?

Independence of Vector Components 2-13** A ball has an initial velocity of 1.3 m/s along the +y direction and starting at to receives an acceleration of 2.10 m/s2 in the +x direction. A) what is the position of the ball at 2.5 sec after to? B) What is the velocity of the ball at that time?