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Trigonometry Identities
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Right Triangle SOHCAHTOA Hypotenuse Side opposite to
Side adjacent to
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Examples Find exact values for all trig function in this triangle: 5 4
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Sines, Cosines, Tangents of Special Angles
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Cofunctions sin (90˚ - ) = cos cos (90˚ - ) = sin
Ex. sin 52 ˚ = cos 48 ˚ = tan (90˚ - ) = cot cot (90˚ - ) = tan Ex. tan 13 ˚= cot 77 ˚ = sec (90˚ - ) = csc csc (90˚ - ) = sec Ex. sec 43 ˚= csc 47 ˚ =
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Fundamental Trig Identities
Reciprocal Identities Quotient Identities
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Pythagorean Identities
(cos , sin ) 1 sin cos sin 2 + cos 2 = 1
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Pythagorean Identities
cos 2 + sin 2 = 1 sin 2 sin 2 sin 2 cot 2 = csc 2 cos 2 cos 2 cos 2 tan 2 = sec 2
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Using Trig Identities Simplify: sin csc 1 Simplify: tan cos
(csc + cot ) (csc - cot ) csc 2 - cot 2 1
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Using a Calculator Find the csc 46.89˚
The calculator does not have csc, so we must use the reciprocal identity
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Applications
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Applications An historic lighthouse is 200 yards from a bike path along the edge of a lake. A walkway to the lighthouse is 400 yards long. Find the acute angle between the bike path and the walkway. = 30˚
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Applications Find the length of a skateboard ramp if the angle from the ground is 18.4˚ and the vertical side is 4 feet high. Ramp = 12.7 ft
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