What is the value of sin(arcsin(3/5)-arctan(12/5)) ?

The value of sin(arcsin(3/5)-arctan(12/5)) is -33/65

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sin(arcsin(3/5)-arctan(12/5))

sin (arcsin (\frac{3}{5}) - arctan (\frac{12}{5}))

- \frac{33}{65}

Solution steps

sin (arcsin (\frac{3}{5}) - arctan (\frac{12}{5}))

Rewrite using trig identities:

sin (arcsin (\frac{3}{5})) cos (arctan (\frac{12}{5})) - cos (arcsin (\frac{3}{5})) sin (arctan (\frac{12}{5}))

= sin (arcsin (\frac{3}{5})) cos (arctan (\frac{12}{5})) - cos (arcsin (\frac{3}{5})) sin (arctan (\frac{12}{5}))

Rewrite using trig identities:

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

Rewrite using trig identities:

cos (arctan (\frac{12}{5})) = \frac{5}{13}

Rewrite using trig identities:

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

Rewrite using trig identities:

sin (arctan (\frac{12}{5})) = \frac{12}{13}

= \frac{3}{5} \cdot \frac{5}{13} - \frac{4}{5} \cdot \frac{12}{13}

Simplify

\frac{3}{5} \cdot \frac{5}{13} - \frac{4}{5} \cdot \frac{12}{13} : - \frac{33}{65}

= - \frac{33}{65}

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

cos (0 + π)

4 sec^{2} (\frac{π}{4}) tan^{2} (\frac{π}{4}) + 2 sec^{4} (\frac{π}{4})

cos (π - 1) \cdot 0.2

\frac{cos ( 0.002 ) - 1}{0.00 2 ^{2}}

What is the value of sin(arcsin(3/5)-arctan(12/5)) ?
The value of sin(arcsin(3/5)-arctan(12/5)) is -33/65