Irrational and transcendental equations

Keywords: Irrational and transcendental equations
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Radical equation

xn=a

Solution:

x=an

Exponential equation

ax=b

Solution:

x=logab=lg blg a

Logarithmic equation

logax=b

Solution:

x=ab=eb·ln a=10b·lg a

Trigonometric equations

sin x=a

Solution:

x1=arc sin a+2kπx2=π-x1


cos x=a

Solution:

x1=arc cos a+2kπx2=π-x1


tg x=a

Solution:

x1=arc tg a+kπ


ctg x=a

Solution:

x1=arc ctg a+kπ

k is an arbitrary integer

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