Trigonometry Trigonometry Why learn Trigonometry Calculate height of

Trigonometry

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

Sense +y (up) -x (left) +x (right) (0, 0) -y (down) -x (left) -y (down) +x (right)

Trigonometry Review Right Triangle A triangle with a 90° angle Sum of all interior angles = 180° Pythagorean Theorem: A 2 + B 2 = C 2 H se u n p) y h ( Opposite Side (opp) te ypo 90° Adjacent Side (adj)

Trigonometry Review Trigonometric Functions soh cah toa sin θ° = opp / hyp cos θ° = adj / hyp tan θ° = opp / adj Opposite Side (opp) te ypo H se u n p) y h ( 90° Adjacent Side (adj)

Trigonometry Application sin θ° = Y / D Y= D sin θ° cos θ° = X / D X = D cos θ° tan θ° = Y / X use D Opposite Side n ote Y p Hy 90° Adjacent Side X

X and Y Components Distance, D Distance = 75 in. Direction = 35° from the horizontal +Y n. i 5 D =7 35° -X -Y adj = X opp = Y +X

X and Y Components Solve for X +Y n. i 5 D =7 35° -X -Y adj = X opp = Y +X

X and Y Components Solve for Y +Y n. i 5 D =7 35° -X -Y adj = X opp = Y +X

Your Turn

Solve for X and Y Components Distance, D Distance = 32 in. Direction = 298° from the horizontal +Y D= -X 298° 32 in. -Y adj = X +X opp = Y

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

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

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