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פּוֹפּוּלָרִי טריגונומטריה >

arcsin(x)=arcsin(2/5)+arcsin(3/5)

פתרון

arcsin (x) = arcsin (\frac{2}{5}) + arcsin (\frac{3}{5})

פתרון

x = \frac{8 + 3 21}{25}

צעדי פתרון

arcsin (x) = arcsin (\frac{2}{5}) + arcsin (\frac{3}{5})

Apply trig inverse properties

arcsin (x) = arcsin (\frac{2}{5}) + arcsin (\frac{3}{5})

arcsin (x) = a \Rightarrow x = sin (a)

x = sin (arcsin (\frac{2}{5}) + arcsin (\frac{3}{5}))

sin (arcsin (\frac{2}{5}) + arcsin (\frac{3}{5})) = \frac{8 + 3 21}{25}

sin (arcsin (\frac{2}{5}) + arcsin (\frac{3}{5}))

Rewrite using trig identities:

sin (arcsin (\frac{2}{5})) cos (arcsin (\frac{3}{5})) + cos (arcsin (\frac{2}{5})) sin (arcsin (\frac{3}{5}))

sin (arcsin (\frac{2}{5}) + arcsin (\frac{3}{5}))

sin (s + t) = sin (s) cos (t) + cos (s) sin (t)

:הפעל זהות של סכום זוויות

= sin (arcsin (\frac{2}{5})) cos (arcsin (\frac{3}{5})) + cos (arcsin (\frac{2}{5})) sin (arcsin (\frac{3}{5}))

= sin (arcsin (\frac{2}{5})) cos (arcsin (\frac{3}{5})) + cos (arcsin (\frac{2}{5})) sin (arcsin (\frac{3}{5}))

Rewrite using trig identities:

sin (arcsin (\frac{2}{5})) = \frac{2}{5}

sin (arcsin (x)) = x :

השתמש בזהות הבאה

= \frac{2}{5}

Rewrite using trig identities:

cos (arcsin (\frac{3}{5})) = \frac{4}{5}

cos (arcsin (\frac{3}{5}))

Rewrite using trig identities:

cos (arcsin (\frac{3}{5})) = 1 - (\frac{3}{5})^{2}

cos (arcsin (x)) = 1 - x^{2} :

השתמש בזהות הבאה

= 1 - (\frac{3}{5})^{2}

= 1 - (\frac{3}{5})^{2}

פשט

= \frac{4}{5}

Rewrite using trig identities:

cos (arcsin (\frac{2}{5})) = \frac{21}{5}

cos (arcsin (\frac{2}{5}))

Rewrite using trig identities:

cos (arcsin (\frac{2}{5})) = 1 - (\frac{2}{5})^{2}

cos (arcsin (x)) = 1 - x^{2} :

השתמש בזהות הבאה

= 1 - (\frac{2}{5})^{2}

= 1 - (\frac{2}{5})^{2}

פשט

= \frac{21}{5}

Rewrite using trig identities:

sin (arcsin (\frac{3}{5})) = \frac{3}{5}

sin (arcsin (x)) = x :

השתמש בזהות הבאה

= \frac{3}{5}

= \frac{2}{5} \cdot \frac{4}{5} + \frac{21}{5} \cdot \frac{3}{5}

\frac{2}{5} \cdot \frac{4}{5} + \frac{21}{5} \cdot \frac{3}{5}

פשט את:

\frac{8 + 3 21}{25}

\frac{2}{5} \cdot \frac{4}{5} + \frac{21}{5} \cdot \frac{3}{5}

\frac{2}{5} \cdot \frac{4}{5} = \frac{8}{25}

\frac{2}{5} \cdot \frac{4}{5}

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

:הכפל שברים

= \frac{2 \cdot 4}{5 \cdot 5}

2 \cdot 4 = 8 :

הכפל את המספרים

= \frac{8}{5 \cdot 5}

5 \cdot 5 = 25 :

הכפל את המספרים

= \frac{8}{25}

\frac{21}{5} \cdot \frac{3}{5} = \frac{3 21}{25}

\frac{21}{5} \cdot \frac{3}{5}

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

:הכפל שברים

= \frac{21 \cdot 3}{5 \cdot 5}

5 \cdot 5 = 25 :

הכפל את המספרים

= \frac{3 21}{25}

= \frac{8}{25} + \frac{3 21}{25}

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

הפעל את החוק

= \frac{8 + 3 21}{25}

= \frac{8 + 3 21}{25}

x = \frac{8 + 3 21}{25}

x = \frac{8 + 3 21}{25}

גרף

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