Why is tan(a) not equal to sin(a)/cos(a)

Question

cpistor 2022-4-24

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https://ww2.mathworks.cn/matlabcentral/answers/1703960-why-is-tan-a-not-equal-to-sin-a-cos-a

回答： Paul 2022-4-25

trying to simplify sin(alpha)/cos(alpha) Matlab does not give tan(alpha), why?

also isolating alpha from b == sin(alpha)/cos(alpha) does not give alpha = atan(b), why?

>> syms alpha b

equ1=b==sin(alpha)/cos(alpha)

simplify(equ1)

equ1=isolate(equ1,alpha)

equ1 =

b == sin(alpha)/cos(alpha)

ans =

b == sin(alpha)/cos(alpha)

equ1 =

alpha == -log((- b^2 - 1)^(1/2)/(b + 1i))*1i

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David Goodmanson 2022-4-24

编辑：David Goodmanson 2022-4-24

Hi cpistor,

to be honest, there are certain situations where Matlab symbolics is not all that bright. But the expression for alpha on your last line is a good expression for atan(b).

( For complex input, the expression does not always exactly agree with atan. Somtimes there is disagreement by pi, reflecting the pi ambiguity in the tan function, i.e. tan(theta) = tan(theta +-pi) )

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