what is sin 1 The inverse sine function sin 1 takes the ratio opposite hypotenuse and gives angle And cosine and tangent follow a similar idea Example lengths are only to one decimal place sin 35 Opposite Hypotenuse 2 8 4 9
The inverse sine function or Sin 1 takes the ratio Opposite Side Hypotenuse Side and produces angle It is also written as arcsin Sin inverse is denoted by sin 1 or arcsin Sin 1 Opposite side Hypotenuse Let us see an example of inverse of sine function Example In a triangle ABC AB 4 9m BC 4 0 m CA 2 8 m and angle B 35 The answer involves the fact that the symbol 1 is used for two different purposes which are confusingly related If c is a number then c 1 is defined to be the reciprocal of c or 1 c That is c 1 1 c We ll see more about this later
what is sin 1
what is sin 1
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The sine function sin of an angle gives the ratio of the perpendicular opposite side of the angle to the hypotenuse Similarly the inverse sine function sin 1 gives the ratio of the hypotenuse to the perpendicular of an angle Sin 1 in radians has a value of 0 8414709848 The inverse sin of 1 ie sin 1 1 is a very special value for the inverse sine function Remember that sin 1 x will give you the angle whose sine is x Therefore sin 1 1 the angle whose sine is 1
In a right angled triangle the sine of an angle is the ratio of its opposite side to the hypotenuse i e sin opposite side hypotenuse Then by the definition of inverse sine sin 1 opposite side hypotenuse Sin 1 x read inverse sine of x and note that the parentheses here are not necessary if you can write the exponent as a superscript is the same as arcsin x Here the input would be a sine ratio and the output would be an angle measure
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Range of the inverse trig functions The trigonometric functions aren t really invertible because they have multiple inputs that have the same output For example sin 0 sin 0 So what should be sin 1 0 A 2 b 2 c 2 2bc cos A Law of Cosines a b a b tan A B 2 tan A B 2 Free math lessons and math homework help from basic math to algebra geometry and beyond Students teachers parents and everyone can find solutions to their math problems instantly
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