What is the value of sin(arctan(-3/4)) ?

The value of sin(arctan(-3/4)) is -3/5

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sin(arctan(-3/4))

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

- \frac{3}{5}

Decimal Notation

- 0.6

Solution steps

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}}

Use the following identity:

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

= \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}}

Simplify

= - \frac{3}{5}

cos (37. 5^{\circ}) sin (7. 5^{\circ})

sin (6 6^{\circ})

1 - cos (2 π)

2 tan (\frac{π}{4})

sec (- 2 π)