標題:
Trigonometric ratio. What is the length of the string?Ans:55.8cm (corr. to 3 sig. fig.)Please show steps clearly.?
發問:
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最佳解答:
Suppose the length of the string is L cm L - L*cos 33° = 9 L( 1 - cos 33° ) = 9 L = 9 / ( 1 - cos 33° ) ≒ 9 / ( 1 - 0.83867 ) = 9 / 0.16133 ≒ 55.8 Ans: 55.8 cm
其他解答:
Trigonometric Ratios "Trigon" is Greek for triangle , and "metric" is Greek for measurement. The trigonometric ratios are special measurements of a right triangle (a triangle with one angle measuring 90°90° ). Remember that the two sides of a right triangle which form the right angle are called the legs , and the third side (opposite the right angle) is called the hypotenuse . There are three basic trigonometric ratios: sine , cosine , and tangent . Given a right triangle, you can find the sine (or cosine, or tangent) of either of the non- 90°90° angles. sine=length of the leg opposite to the anglelength of hypotenuse abbreviated "sin"cosine=length of the leg adjacent to the anglelength of hypotenuse abbreviated "cos"tangent=length of the leg opposite to the anglelength of the leg adjacent to the angle abbreviated "tan"sine=length of the leg opposite to the anglelength of hypotenuse abbreviated "sin"cosine=length of the leg adjacent to the anglelength of hypotenuse abbreviated "cos"tangent=length of the leg opposite to the anglelength of the leg adjacent to the angle abbreviated "tan" Example: Write expressions for the sine, cosine, and tangent of ∠A∠A . The length of the leg opposite ∠A∠A is aa . The length of the leg adjacent to ∠A∠A is bb , and the length of the hypotenuse is cc . The sine of the angle is given by the ratio "opposite over hypotenuse." So, sin∠A=acsin∠A=ac The cosine is given by the ratio "adjacent over hypotenuse." cos∠A=bccos∠A=bc The tangent is given by the ratio "opposite over adjacent." tan∠A=abtan∠A=ab Generations of students have used the mnemonic " SOHCAHTOA " to remember which ratio is which. ( S ine: O pposite over H ypotenuse, C osine: A djacent over H ypotenuse, T angent: O pposite over A djacent.) Other Trigonometric Ratios The other common trigonometric ratios are: secant=length of hypotenuselength of the leg adjacent to the angle abbreviated "sec" sec(x)=1cos(x)cosecant=length of hypotenuselength of the leg opposite to the angle abbreviated "csc" csc(x)=1sin(x)secant=length of the leg adjacent to the anglelength of the leg opposite to the angle abbreviated "cot" cot(x)=1tan(x)secant=length of hypotenuselength of the leg adjacent to the angle abbreviated "sec" sec(x)=1cos(x)cosecant=length of hypotenuselength of the leg opposite to the angle abbreviated "csc" csc(x)=1sin(x)secant=length of the leg adjacent to the anglelength of the leg opposite to the angle abbreviated "cot" cot(x)=1tan(x) Example: Write expressions for the secant, cosecant, and cotangent of ∠A∠A . The length of the leg opposite ∠A∠A is aa . The length of the leg adjacent to ∠A∠A is bb , and the length of the hypotenuse is cc . The secant of the angle is given by the ratio "hypotenuse over adjacent". So, sec∠A=cbsec∠A=cb The cosecant is given by the ratio "hypotenuse over opposite". csc∠A=cacsc∠A=ca The cotangent is given by the ratio "adjacent over opposite". cot∠A=ba https://www.varsitytutors.com/hotmath/hotmath_help/topics/trigonometric-ratios
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