# 4.3 Cont. FUNDAMENTAL TRIG IDENTITIES Reciprocal Identities sinθ

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```					4.3 Cont. FUNDAMENTAL TRIG IDENTITIES Reciprocal Identities sinθ = 1 cosθ = 1 tanθ = 1 cscθ secθ cotθ cscθ = 1 sinθ secθ = 1 cosθ cotθ = 1 tanθ

Quotient Identities tanθ = sinθ cotθ = cosθ cosθ sinθ Pythagorean Identities sin2θ + cos2θ = 1 1 + tan2θ = sec2 θ 1 + cot2θ = csc2 θ Ex. 1 Let θ be an acute angle such that sinθ =0.6. Find the values of a) cosθ = b) tanθ =
Title: Nov 8­9:25 AM (1 of 4)

*using trig identities a) sin2θ + cos2θ = 1 (0.6)2 + cos2θ = 1 cos2θ = 1-(0.6)2 cos2θ = .64 cosθ = 0.8 b) tanθ = sinθ = 0.6 = 0.75 cosθ 0.8 Ex. 2 Let θ be an acute angle such that tanθ = 3. Find the values of: a) cotθ = b) secθ =

Title: Nov 8­10:01 AM (2 of 4)

*Evaluating trig functions with a calculator be sure if angle is measured in degrees that you set your calculator to degree mode ( same with radians). Ex. 3 a) cos 28 = b) sec 28 = Ex. 4 Use a calculator to evaluate sec(5 40'12") = Ex. 5 p. 385 #7 A surveyor is standing 50 feet from the base of a large tree. The surveyor measures the angle of elevation to the top of the tree as 71.5 . How tall is the tree?

Title: Nov 8­10:08 AM (3 of 4)

Ex. 6 p. 385 #8 A person is 200 yards from a river. Rather than walking directly to the river, the person walks 400 yards along a straight path to the river's edge. Find the acute θ between this path and the river's edge.

Ex. 7 p. 386 #9 A 12 meter flagpole casts a 9 meter shadow. Find the θ of elevation of the sun.

Ex. 8 Find values of θ in degrees and radians. a) sinθ = 0.8191 b) cosθ = 0.0175 ASSN: p. 388-390 23-67 odd
Title: Nov 8­10:17 AM (4 of 4)

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