Irrational and transcendental equations

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

Keywords: Irrational and transcendental equations