M1410407Part2

M1410407Part2 - (Section 4.7: Inverse Trig Functions) 4.82...

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Unformatted text preview: (Section 4.7: Inverse Trig Functions) 4.82 PART F: EVALUATING INVERSE TRIG FUNCTIONS Think: A trig function such as sin takes in angles (i.e., real numbers in its domain) as inputs and “spits out” outputs that are trig values (for sin, values between − 1 and 1, inclusive). On the other hand, an inverse trig function such as sin − 1 takes in trig values as inputs and “spits out” angles as outputs. These angles must be in the range. Warning: Although calculators can provide sin − 1 values and other inverse trig values using degree measure, it is conventional to use radian measure, instead, since they directly correspond to “real numbers.” (Section 4.7: Inverse Trig Functions) 4.83 Example Evaluate sin − 1 1 ( ) , or arcsin1 . Solution We know that sin π 2 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ = 1 . Although there are other angles whose sine is 1, π 2 is the only one that is a “legal” output of sin − 1 , because it is the only one in the range of sin − 1 , namely − π 2 , π 2 ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ . Therefore, sin − 1 1 ( ) = ! 2 . Example Evaluate sin − 1 − 2 2 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ , or arcsin − 2 2 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ . Solution What angle in the range of sin − 1 , − π 2 , π 2 ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ , has a sin value of − 2 2 ?...
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This note was uploaded on 02/07/2012 for the course MATH 2203 taught by Professor Ellermeyer during the Fall '10 term at FIU.

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M1410407Part2 - (Section 4.7: Inverse Trig Functions) 4.82...

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