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Popular >

sin(arcsin(1/4)+arctan(-5))

Solution

sin (arcsin (\frac{1}{4}) + arctan (- 5))

Solution

\frac{26 - 5 390}{104}

+1

Solution steps

sin (arcsin (\frac{1}{4}) + arctan (- 5))

Use the following property:

arctan (- x) = - arctan (x)

arctan (- 5) = - arctan (5)

= sin (arcsin (\frac{1}{4}) - arctan (5))

Rewrite using trig identities:

sin (arcsin (\frac{1}{4})) cos (arctan (5)) - cos (arcsin (\frac{1}{4})) sin (arctan (5))

= sin (arcsin (\frac{1}{4})) cos (arctan (5)) - cos (arcsin (\frac{1}{4})) sin (arctan (5))

Rewrite using trig identities:

sin (arcsin (\frac{1}{4})) = \frac{1}{4}

Rewrite using trig identities:

cos (arctan (5)) = \frac{26}{26}

Rewrite using trig identities:

cos (arcsin (\frac{1}{4})) = \frac{15}{4}

Rewrite using trig identities:

sin (arctan (5)) = \frac{5 26}{26}

= \frac{1}{4} \cdot \frac{26}{26} - \frac{15}{4} \cdot \frac{5 26}{26}

Simplify

\frac{1}{4} \cdot \frac{26}{26} - \frac{15}{4} \cdot \frac{5 26}{26} : \frac{26 - 5 390}{104}

= \frac{26 - 5 390}{104}

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Frequently Asked Questions (FAQ)

What is the value of sin(arcsin(1/4)+arctan(-5)) ?
The value of sin(arcsin(1/4)+arctan(-5)) is (sqrt(26)-5sqrt(390))/(104)