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)
Right Triangle Has 3 sides: Hypotenuse Adjacent Opposite 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 hyp 3 5 sin B = 5 3 opp hyp 4 5 sin C = B 4
Cosine Cosine is the ratio of the adjacent side divided by the hypotenuse. C adj hyp 4 5 cos B = 5 3 adj hyp 3 5 cos C = B 4
Tangent C opp 3 adj tan B = 4 5 3 opp 4 adj tan C = 3 B 4 tangent is the ratio of the opposite side divided by the adjacent. C opp adj 3 4 tan B = 5 3 opp adj 4 3 tan C = B 4
What’s up with the sayings Some old horse, caught another horse, taking oats away. opp hyp adj hyp opp adj sin = cos = tan =
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 6 j opp adj 3 6 tan J = 3 45 k
Find cos j l 6 j adj hyp 6 45 cos J = 3 45 now simplify k
Find tan k l 12 j opp adj 12 5 tan K = 5 13 k
Find sin k l 12 j opp hyp 12 13 sin K = 5 13 k
Find cos k l 12 j adj hyp 5 13 cos K = 5 13 k