What is the value of sin(1035) ?

The value of sin(1035) is -(sqrt(2))/2

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sin(1035)

sin (103 5^{\circ})

- \frac{2}{2}

Solution steps

sin (103 5^{\circ})

sin (103 5^{\circ}) = sin (31 5^{\circ})

= sin (31 5^{\circ})

Rewrite using trig identities:

sin (18 0^{\circ}) cos (13 5^{\circ}) + cos (18 0^{\circ}) sin (13 5^{\circ})

= sin (18 0^{\circ}) cos (13 5^{\circ}) + cos (18 0^{\circ}) sin (13 5^{\circ})

Use the following trivial identity:

sin (18 0^{\circ}) = 0

Use the following trivial identity:

cos (13 5^{\circ}) = - \frac{2}{2}

Use the following trivial identity:

cos (18 0^{\circ}) = (- 1)

Use the following trivial identity:

sin (13 5^{\circ}) = \frac{2}{2}

= 0 \cdot (- \frac{2}{2}) + (- 1) \frac{2}{2}

Simplify

= - \frac{2}{2}

sin^{4} (9 0^{\circ})

6 + 3 cos (0)

cos (6 0^{\circ}) + sin (6 0^{\circ})

tan^{2} (57. 5^{\circ})

1 - 2 sin^{2} (\frac{π}{6})