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Popular >

sin(arcsin(1/2)+arctan(-4))

Solution

sin (arcsin (\frac{1}{2}) + arctan (- 4))

Solution

\frac{17}{34} - \frac{2 51}{17}

+1

Solution steps

sin (arcsin (\frac{1}{2}) + arctan (- 4))

Use the following property:

arctan (- x) = - arctan (x)

arctan (- 4) = - arctan (4)

= sin (arcsin (\frac{1}{2}) - arctan (4))

Rewrite using trig identities:

sin (arcsin (\frac{1}{2})) cos (arctan (4)) - cos (arcsin (\frac{1}{2})) sin (arctan (4))

= sin (arcsin (\frac{1}{2})) cos (arctan (4)) - cos (arcsin (\frac{1}{2})) sin (arctan (4))

Rewrite using trig identities:

sin (arcsin (\frac{1}{2})) = \frac{1}{2}

Rewrite using trig identities:

cos (arctan (4)) = \frac{17}{17}

Rewrite using trig identities:

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

Rewrite using trig identities:

sin (arctan (4)) = \frac{4 17}{17}

= \frac{1}{2} \cdot \frac{17}{17} - \frac{3}{2} \cdot \frac{4 17}{17}

Simplify

\frac{1}{2} \cdot \frac{17}{17} - \frac{3}{2} \cdot \frac{4 17}{17} : \frac{17}{34} - \frac{2 51}{17}

= \frac{17}{34} - \frac{2 51}{17}

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Frequently Asked Questions (FAQ)

What is the value of sin(arcsin(1/2)+arctan(-4)) ?
The value of sin(arcsin(1/2)+arctan(-4)) is (sqrt(17))/(34)-(2sqrt(51))/(17)