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עברית

العربية

(sin(-20))/(cos(380))+tan(200)

Soluzione

\frac{sin ( - 2 0 ^{\circ} )}{cos ( 38 0 ^{\circ} )} + tan (20 0^{\circ})

0

Fasi della soluzione

\frac{sin ( - 2 0 ^{\circ} )}{cos ( 38 0 ^{\circ} )} + tan (20 0^{\circ})

Semplificare

= \frac{sin ( - 2 0 ^{\circ} ) + tan ( 20 0 ^{\circ} ) cos ( 38 0 ^{\circ} )}{cos ( 38 0 ^{\circ} )}

Usare la proprietà seguente:

sin (- x) = - sin (x)

sin (- 2 0^{\circ}) = - sin (2 0^{\circ})

= \frac{- sin ( 2 0 ^{\circ} ) + tan ( 20 0 ^{\circ} ) cos ( 38 0 ^{\circ} )}{cos ( 38 0 ^{\circ} )}

tan (20 0^{\circ}) = tan (2 0^{\circ})

tan (20 0^{\circ})

Riscrivi

20 0^{\circ}

come

18 0^{\circ} + 2 0^{\circ}

= tan (18 0^{\circ} + 2 0^{\circ})

Applicare la periodicità di

tan

tan (x + 18 0^{\circ}) = tan (x)

tan (18 0^{\circ} + 2 0^{\circ}) = tan (2 0^{\circ})

= tan (2 0^{\circ})

= \frac{- sin ( 2 0 ^{\circ} ) + tan ( 2 0 ^{\circ} ) cos ( 38 0 ^{\circ} )}{cos ( 38 0 ^{\circ} )}

cos (38 0^{\circ}) = cos (2 0^{\circ})

cos (38 0^{\circ})

Riscrivi

38 0^{\circ}

come

36 0^{\circ} + 2 0^{\circ}

= cos (36 0^{\circ} + 2 0^{\circ})

Applicare la periodicità di

cos

cos (x + 36 0^{\circ}) = cos (x)

cos (36 0^{\circ} + 2 0^{\circ}) = cos (2 0^{\circ})

= cos (2 0^{\circ})

= \frac{- sin ( 2 0 ^{\circ} ) + tan ( 2 0 ^{\circ} ) cos ( 2 0 ^{\circ} )}{cos ( 38 0 ^{\circ} )}

cos (38 0^{\circ}) = cos (2 0^{\circ})

cos (38 0^{\circ})

Riscrivi

38 0^{\circ}

come

36 0^{\circ} + 2 0^{\circ}

= cos (36 0^{\circ} + 2 0^{\circ})

Applicare la periodicità di

cos

cos (x + 36 0^{\circ}) = cos (x)

cos (36 0^{\circ} + 2 0^{\circ}) = cos (2 0^{\circ})

= cos (2 0^{\circ})

= \frac{- sin ( 2 0 ^{\circ} ) + tan ( 2 0 ^{\circ} ) cos ( 2 0 ^{\circ} )}{cos ( 2 0 ^{\circ} )}

Riscrivere utilizzando identità trigonometriche:

tan (2 0^{\circ}) = \frac{sin ( 2 0 ^{\circ} )}{cos ( 2 0 ^{\circ} )}

tan (2 0^{\circ})

Usare l'identità trigonometrica di base:

tan (x) = \frac{sin ( x )}{cos ( x )}

= \frac{sin ( 2 0 ^{\circ} )}{cos ( 2 0 ^{\circ} )}

= \frac{- sin ( 2 0 ^{\circ} ) + \frac{s i n ( 2 0 ^{\circ} )}{c o s ( 2 0 ^{\circ} )} cos ( 2 0 ^{\circ} )}{cos ( 2 0 ^{\circ} )}

Semplificare

= 0

cot (- \frac{4 π}{3})

cos (0.3)

arctan (\frac{5}{1})

tan (\frac{π}{3} + \frac{π}{4})

sin (3 0^{\circ} + 4 5^{\circ})