What is the value of sin(pi/2+(13pi)/(12)) ?

The value of sin(pi/2+(13pi)/(12)) is (sqrt(2)(-1-sqrt(3)))/4

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sin(pi/2+(13pi)/(12))

sin (\frac{π}{2} + \frac{13 π}{12})

\frac{2 ( - 1 - 3 )}{4}

Solution steps

sin (\frac{π}{2} + \frac{13 π}{12})

Simplify:

\frac{π}{2} + \frac{13 π}{12} = \frac{19 π}{12}

= sin (\frac{19 π}{12})

Rewrite using trig identities:

sin (\frac{5 π}{6}) cos (\frac{3 π}{4}) + cos (\frac{5 π}{6}) sin (\frac{3 π}{4})

= sin (\frac{5 π}{6}) cos (\frac{3 π}{4}) + cos (\frac{5 π}{6}) sin (\frac{3 π}{4})

Use the following trivial identity:

sin (\frac{5 π}{6}) = \frac{1}{2}

Use the following trivial identity:

cos (\frac{3 π}{4}) = - \frac{2}{2}

Use the following trivial identity:

cos (\frac{5 π}{6}) = - \frac{3}{2}

Use the following trivial identity:

sin (\frac{3 π}{4}) = \frac{2}{2}

= \frac{1}{2} (- \frac{2}{2}) + (- \frac{3}{2}) \frac{2}{2}

Simplify

\frac{1}{2} (- \frac{2}{2}) + (- \frac{3}{2}) \frac{2}{2} : \frac{2 ( - 1 - 3 )}{4}

= \frac{2 ( - 1 - 3 )}{4}

cos (9 3^{\circ})

\frac{1 - sin ( 3 7 ^{\circ} )}{1 + sin ( 3 7 ^{\circ} )}

tan^{2} (4 5^{\circ}) - cos (3 0^{\circ})

sin (- 5 0^{\circ})

cos (arctan (\frac{5}{12}) - arcsec (\frac{9}{7}))

What is the value of sin(pi/2+(13pi)/(12)) ?
The value of sin(pi/2+(13pi)/(12)) is (sqrt(2)(-1-sqrt(3)))/4