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פּוֹפּוּלָרִי טריגונומטריה >

cos(arctan(-3/4)-arcsin(4/5))

פתרון

cos (arctan (- \frac{3}{4}) - arcsin (\frac{4}{5}))

פתרון

0

צעדי פתרון

cos (arctan (- \frac{3}{4}) - arcsin (\frac{4}{5}))

arctan (- x) = - arctan (x) :

השתמש בחוק הבא

arctan (- \frac{3}{4}) = - arctan (\frac{3}{4})

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

cos (- x) = cos (x) :

השתמש בחוק הבא

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

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

Rewrite using trig identities:

cos (arctan (\frac{3}{4})) cos (arcsin (\frac{4}{5})) - sin (arctan (\frac{3}{4})) sin (arcsin (\frac{4}{5}))

cos (arctan (\frac{3}{4}) + arcsin (\frac{4}{5}))

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

:הפעל זהות של סכום זוויות

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

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

Rewrite using trig identities:

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

cos (arctan (\frac{3}{4}))

Rewrite using trig identities:

cos (arctan (\frac{3}{4})) = \frac{1 + ( \frac{3}{4} ) ^{2}}{1 + ( \frac{3}{4} ) ^{2}}

cos (arctan (x)) = \frac{1 + x ^{2}}{1 + x ^{2}} :

השתמש בזהות הבאה

= \frac{1 + ( \frac{3}{4} ) ^{2}}{1 + ( \frac{3}{4} ) ^{2}}

= \frac{1 + ( \frac{3}{4} ) ^{2}}{1 + ( \frac{3}{4} ) ^{2}}

פשט

= \frac{4}{5}

Rewrite using trig identities:

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

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

Rewrite using trig identities:

cos (arcsin (\frac{4}{5})) = 1 - (\frac{4}{5})^{2}

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

השתמש בזהות הבאה

= 1 - (\frac{4}{5})^{2}

= 1 - (\frac{4}{5})^{2}

פשט

= \frac{3}{5}

Rewrite using trig identities:

sin (arctan (\frac{3}{4})) = \frac{3}{5}

sin (arctan (\frac{3}{4}))

Rewrite using trig identities:

sin (arctan (\frac{3}{4})) = \frac{( \frac{3}{4} ) 1 + ( \frac{3}{4} ) ^{2}}{1 + ( \frac{3}{4} ) ^{2}}

sin (arctan (x)) = \frac{x 1 + x ^{2}}{1 + x ^{2}} :

השתמש בזהות הבאה

= \frac{( \frac{3}{4} ) 1 + ( \frac{3}{4} ) ^{2}}{1 + ( \frac{3}{4} ) ^{2}}

= \frac{\frac{3}{4} 1 + ( \frac{3}{4} ) ^{2}}{1 + ( \frac{3}{4} ) ^{2}}

פשט

= \frac{3}{5}

Rewrite using trig identities:

sin (arcsin (\frac{4}{5})) = \frac{4}{5}

sin (arcsin (x)) = x :

השתמש בזהות הבאה

= \frac{4}{5}

= \frac{4}{5} \cdot \frac{3}{5} - \frac{3}{5} \cdot \frac{4}{5}

פשט

= 0

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