P a g e 68 In a right triangle as an acute angle gets smaller A the cosine gets

# P a g e 68 in a right triangle as an acute angle gets

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P a g e68.In a right triangle, as an acute angle gets smaller, ______________________.A.the cosine gets closer to 1 and the sine gets closer to 0B.the sine gets closer to 1 and the cosine gets closer to 0C.the cosine gets closer to 0 and the tangent gets closer to 1D.the tangent gets closer to 0 and the sine gets closer to 1The Tangent, Sine and Cosine RatiosAtrigonometric ratiois a ratio of the lengths of two sides of a right triangle.The three ratios are given below forA. Note that the tangent of A is usually abbreviatedtan A, the sine ofA is usually abbreviatedsin A, and the cosine of A is usually abbreviatedcos A.SOH-CAH-TOA:sin A =cahypotenusetheoflengthlegoppositetheoflengthcos A =cbhypotenusetheoflengthlegadjacenttheoflengthtan A =balegadjacenttheoflengthlegoppositetheoflengthInABC, a, b, and c are always positive and c is always greater than a or b. Thus, the ratiocaorcbranges between 0 and 1. As angle A gets smaller, angle B gets larger and consequently, side a gets shorterand side b gets longer. Thus, as angle A gets smaller,cabecomes smaller and gets closer to 0 andcbbecomes larger and gets closer to 1. The conclusion is the same as inchoice letter A:the cosine gets closerto 1 and the sine gets closer to 0. What happens toba? Since a gets shorter and b gets longer,baor tan Agets smaller and it approaches 0.Also, tan A =BAcossin. Thus, as angle A gets smaller, sin A gets closer to 0 and cos A gets closer to 1, tan A=BAcossin100.The answer isA.abcCBAhypotenuseopposite legadjacent leg
REVIEW MASTERSTMMATH REVIEW©2011115 |P a g e69.In the figure the right triangle has side lengths a, b, and c, where cis the length of the hypotenuse. a2can be found by70.Which of the following is equal to sin?Since theabove is a right,Pythagorean Theoremapplies:a2+ b2= c2Solving fora2,a2= c2– b2(subtracta2from each side of the formula). This is not the same asChoice letter A(adding b2and c2). Neither it is thesquare of the sum of b andc (Choice letter B)The answer isD.InABC,sin=cacos=cbtan=ba
REVIEW MASTERSTMMATH REVIEW©2011116 |P a g eCHAPTER 8: Circles