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Published byOwen Sims Modified over 9 years ago
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It must be one to one … pass the horizontal line test Will a sine, cosine, or tangent function have an inverse? Their inverses are defined over the following intervals: Sine: [ -π/2, π/2 ] Cosine: [ 0, π ] Tangent: [ -π/2, π/2 ]
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y = sin -1 x or y = arcsin x i.o.i sin y = x y = cos -1 x or y = arccos x y = tan -1 x or y = arctan x Their graphs are on pg 324 if you would like to reference them
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1.) 2.)
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1.) 2.) 3.) It will be helpful to remember: sinθ = y then arcsin y = θ cos θ = x then arccos x = θ
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To do this on your calculator… ▪ 2 nd shift then trig function ▪ The steps are on page 325 if you need a refresher ▪ Let’s practice…. ▪ Pg. 328 #’s 2 – 26 even
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Pg. 328 #’s 1 – 41 odd
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Compositions of Functions f (f -1 (x) ) = ? f -1 ( f(x) ) = ? Therefore: sin(arcsin x) = xarcsin(sin y) = y cos(arccos x) = xarccos(cos y) = y tan(arctan x) = xarctan(tan y) = y *remember - only works over certain intervals… ▪ Refer to page 326
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Use the co-terminal angles that are in the range! Let’s practice: 1) arcsin[sin (π/2) ] = ? 2) arccos[cos (π/6) ] = ? 3) tan[arctan (-5)] = ? 4) arcsin[sin (-π/4)]= ?
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5) arcsin(sin 5π/3 ) = ? 6) sin(arcsin π ) = ? 7) arctan (tan π/6) = ? 8) tan(arcsin √2/2)=? Pg. 328 #’s 44, 46, 48
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Ex. 1) Find the exact value of tan(arccos 2/3) ▪ Use a right triangle
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2.) sin(arccos √5/ 5) 3.) csc[arctan(-5/12)]
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Ex.1) sin(arccos 3x) ; 0 ≤ x ≤ 1/3 Ex 2) cot(arcsin 2x) ; 0 ≤ x ≤ 1/3 Practice pg. 328 #’s 60, 64, 66, 68
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Pg. 328 #’s 47-73 odd, 91, 95
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