GREEKS USED TRIGONOMETRY TO MEASURE THE DISTANCE TO

GREEKS USED TRIGONOMETRY TO MEASURE THE DISTANCE TO THE STARS fguilbert

In 140 BC Hipparchus BEGAN TO USE TRIGONOMETR Y fguilbert

TRIGONOMETRY GREEK WORD MEANING: TRIANGLE MEASURE fguilbert

WE WILL USE ONLY RIGHT TRIANGLES 90 fguilbert

HY PO SIDE TE NU OPPOSITE S <B E B ADJACENT to < fguilbert

The Sine Cosine & Tangent are ratios between 2 sides of a right triangle. The angles are related to those ratios. fguilbert

OPP HYP ADJ SIN B = OPP HYP fguilbert B S=O H

OPP HYP ADJ COS B = ADJ HYP fguilbert B C=A H

OPP HYP ADJ TAN B = OPP ADJ fguilbert B T=O A

B Choosing the Sin Cos or Tan depends on C the information you have. Ø SINØ = B/C opp/hyp fguilbert

A/C COSØ = adj/hyp C A Ø fguilbert

B A Ø B/A TAN Ø = opp/adj fguilbert

30 8 X We use trig to find missing angles and side fguilbert

You have opp and hyp Sin = opp/hyp 30 Sin 8 X opp fguilbert o 30 =X 8. 5 = X/8 4=X

You have the adj and hyp Cos = adj/hyp 30 Y adj 8 Cos fguilbert o 30 = Y 8 8 Cos 30 = Y 6. 9= Y

Tan = opp/adj Tan X = X 6 adj 4 opp 4 6 Tan X =. 666 -1 Tan. 666= X 0 33. 7 = X fguilbert

S=O/H C=A/H T=O/A Soh. Cah. Toa - Name Use the letters to remember sin cosine & tangent ratios fguilbert

S =O Sin Opp H Hyp C A Cos = Adj Hyp H Tan = O Opp T A Adj SOH CAH TOA fguilbert

Soh. Cah. Toa was a native Amerivan with broken teepees. To fix them he used sin cos tan. fguilbert

S=O/H C=A/H Some Old Horse Caught A Horse Taking Oats Away fguilbert T=O/A

Find X Which one uses adj and o 0 30 Tan = X/ 20 20 Tan 30 = X 20 11. 5 = X adj 30 fguilbert x opp

Find Y cos = adj/hyp 0 30 cos = Y/20 20 Cos 30 = Y adj Y 30 17. 32 = Y fguilbert 20 hyp

s = o/h X Sin = hyp 10 10 10 Sin 62 = X o 62 X opp 8. 829 = X o 62 fguilbert

To find the angle use 2 nd function tan Tan N = 5/4 5 = 1. 25 opp N Tan-1 1. 25 = N 0 4 51. 3 = N adj fguilbert

APPLICATIONS: A plane flying at 5. 68 miles starts its descent 130 miles from the airport. At what angle should the plane descend? fguilbert

Angle of Descent Ø 5. 68 mi. 130 Mi. fguilbert Ø

Ø is in 2 places alt int <’s = tan Ø = 5. 68 130 Ø 5. 68 mi. 130 Mi. fguilbert Ø

tan Ø = 5. 68 130 tan Ø =. 0437 -1 tan. 0437 fguilbert = 0 2. 5

Questions? fguilbert

Thought for the day The most important human endeavor is striving for morality in our actions. fguilbert