Trigonometry Computer Integrated Manufacturing © 2013 Project Lead The Way, Inc.

Trigonometry Why learn Trigonometry? Calculate height of object Without climbing the tree! Plan geometry for shuttle space arm θ = 37O Opp Adj = 53 ft Hyp

Sense +y (up) +y (up) -x (left) +x (right) -y (down) -y (down) (0,0) -y (down) -y (down) When there is more than one vector force and they are added together, it is crucial to keep track of sense. The standard convention is that right in the X direction is a positive number, and X in the left direction is a negative number. Y in the up direction is positive, and Y in the down direction is negative. -x (left) +x (right)

Trigonometry Review Right Triangle A triangle with a 90° angle Sum of all interior angles = 180° Pythagorean Theorem: A2 + B2 = C2 Hypotenuse (hyp) 90° Opposite Side (opp) Adjacent Side (adj)

Trigonometry Review Trigonometric Functions soh cah toa sin θ° = opp / hyp cos θ° = adj / hyp tan θ° = opp / adj Hypotenuse (hyp) 90° Opposite Side (opp) Adjacent Side (adj)

Trigonometry Application sin θ° = Y / D cos θ° = X / D tan θ° = Y / X Y= D sin θ° X = D cos θ° Hypotenuse D 90° Opposite Side Y Adjacent Side X

X and Y Components Distance, D Distance = 75 in. Direction = 35° from the horizontal +Y When the X and Y components are calculated, it can be assumed that the X component will have a higher value because the vector is closer to the horizontal than the vertical. D = 75 in. opp = Y 35° -X +X adj = X -Y

X and Y Components Solve for X D = 75 in. opp = Y 35° adj = X +Y -X +X

X and Y Components Solve for Y D = 75 in. opp = Y 35° adj = X +Y -X +X

Your Turn Students will solve this next problem.

Solve for X and Y Components Distance, D Distance = 32 in. Direction = 298° from the horizontal +Y 298° -X +X When the X and Y components are calculated, it can be assumed that the Y component will have a higher value because the vector is closer to the vertical than the horizontal. Note that Y will be negative. Referencing the +X axis and measuring counterclockwise allows the trigonometric functions to automatically account for a positive or negative result. D = 32 in. opp = Y adj = X -Y

X and Y Components Solve for X 298° D = 32 in. opp = Y adj = X +Y -X

X and Y Components Solve for Y 298° D = 32 in. opp = Y adj = X +Y -X Note that the Y value is negative. D = 32 in. opp = Y adj = X -Y

References National Aeronautics and Space Administration (NASA). (2010). Retrieved May 5, 2010, from http://grin.hq.nasa.gov