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Basic Trig New Words Trigonometry: the study of the properties of triangles. Trigonometric ratio: ratio of the measures of 2 sides of a triangle. New Words Sine: written sin, read [sahyn] Cosine: written cos, read [koh-sahyn] Tangent: written tan, read [tan- juhnt) New sayings Some old horse, caught another horse, taking oats away. Signs of happiness come after having tankards of ale. Some of her children are having trouble over algebra. Some out houses can actually have totally odorless aromas. SOH CAH TOA (read soh-kuh-toh-uh) Has 3 sides: Hypotenuse Adjacent Opposite Right Triangle The Hypotenuse is always across from the right angle. It is the longest. The other two will depend on what angle we are dealing with Right Triangle The opposite side is across the triangle from the angle. The adjacent side is next to the angle. It is one of the sides of the angle. Right Triangle Hypotenuse Adjacent Opposite If we are talking about this angle then... Right Triangle Hypotenuse Adjacent Opposite If we are talking about this angle then... Sine Sine is the ratio of the opposite side divided by the hypotenuse. C opp sin B = hyp 5 3 opp sin C = B hyp 4 3 5 4 5 Cosine Cosine is the ratio of the adjacent side divided by the hypotenuse. C adj cos B = hyp 5 3 adj cos C = B hyp 4 4 5 3 5 Tangent tangent is the ratio of the opposite side divided by the adjacent. C 5 B 4 3 opp 3 tan B = adj 4 opp 4 tan C = adj 3 What’s up with the sayings Some old horse, caught another horse, taking oats away. opp sin = hyp adj cos = hyp opp tan = adj Which ever one you like... Some old horse, caught another horse, taking oats away. Signs of happiness come after having tankards of ale. Some of her children are having trouble over algebra. Some out houses can actually have totally odorless aromas. SOH CAH TOA (read soh-kuh-toh-uh) soak-a-toe-a Find tan j l 3 k 6 j 45 opp 3 tan J = adj 6 Find cos j l 3 k 6 j 45 adj 6 cos J = hyp 45 now simplify Find tan k l 5 k 12 13 j opp 12 tan K = adj 5 Find sin k l 5 k 12 13 j opp 12 sin K = hyp 13 Find cos k l 5 k 12 13 j adj 5 cos K = hyp 13