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

2. 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

3. 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)

4. 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)

5. 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)

6. 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

7. 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

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

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

10. Your Turn
Students will solve this next problem.

11. 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

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

13. 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

14. References
National Aeronautics and Space Administration (NASA). (2010). Retrieved May 5, 2010, from