Right Triangle Trigonometry hypotenuse hypotenuse opposite adjacent adjacent opposite reciprocal functions *** “SOH CAH TOA” ***

Right Triangle Trigonometry, cont. Find the six trig functions for the given triangle. 1. Find the missing side measurement: Recall the Pythagorean Theorem: c2 = a2 + b2 hyp side side 5 c2 = 32 + 42 4 c2 = 9 + 16 c2 = 25 c = 5 hyp 3 2. Find the six trig functions “SOH CAH TOA” opp hyp

Common Pythagorean Triples (CPT’s) **memorize!!!** 3, 4, 5 5, 12, 13 8, 15, 17 7, 24, 25 & multiples 6, 8, 10 10, 24, 26 16, 30, 34 14, 48, 50 9, 12, 15 etc.

Special Right Triangles 45o – 45o – 90o 30o – 60o – 90o 45o 30o 2 1 45o 60o 1 1 **memorize** ex. sin 60o = NOTICE: sin 60o = ex. cos 45o = ex. tan 30o =

csc und. sec 1 und. cot und. 1 2 3 4 4 3 2 1 degrees radians undefined 1 2 3 4 (y) 4 3 2 1 (x) undefined csc und. recip-rocals of above sec 1 und. cot und.

Cofunctions not the same as reciprocal functions NOTICE: sin 30o = = cos 60o (because 30o and 60o are complementary angles) In general cofunctions of complementary angles are equal. Ex. sin 40o = cos 50o cot 35o = tan 55o etc.

Fundamental Trigonometric Identities **memorize** Reciprocal Identities: Quotient Identities: Pythagorean Identities: y2 + x2 = 1 (unit circle) leg2 + leg2 = 1

How to remember Pythagorean Identities clue: pythagorean *memorize this one 3 Then, by alg: Also: 3 And: Also: 3 And: 3 groups of 3: 9 total

Examples find the values of cos and tan .62 + x2 = 1 .36 + x2 = 1 y2 + x2 = 1 .62 + x2 = 1 .6 opp. .36 + x2 = 1 (sin) (y) x2 = .64 x = .8 now know all 3 parts of so cos = .8 And tan

Examples, cont. Use trigonometric identities to transform one side of the equation to the other. **work on ONE side ONLY** Do NOT operate across the = sign

Examples, cont. Solve: tan 71.5 = 50 tan 71.5 = x 400 yd x 71.5o hyp. x opp. 71.5o 200 yd. opp. 50 ft. adj. So use sin: So use tan: tan 71.5 = *When looking for an angle use inverse trig function i.e. where does sin theta = 1/2 50 tan 71.5 = x

Examples, cont. Find the value of in degrees and radians. Evaluate: tan 33.5o *When looking for an angle use inverse trig function radians: