What is the value of sin(-(7pi)/6)+cos(-pi/4) ?

The value of sin(-(7pi)/6)+cos(-pi/4) is (1+sqrt(2))/2

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sin(-(7pi)/6)+cos(-pi/4)

sin (- \frac{7 π}{6}) + cos (- \frac{π}{4})

\frac{1 + 2}{2}

Solution steps

sin (- \frac{7 π}{6}) + cos (- \frac{π}{4})

Use the following property:

cos (- x) = cos (x)

cos (- \frac{π}{4}) = cos (\frac{π}{4})

= sin (- \frac{7 π}{6}) + cos (\frac{π}{4})

Use the following property:

sin (- x) = - sin (x)

sin (- \frac{7 π}{6}) = - sin (\frac{7 π}{6})

= - sin (\frac{7 π}{6}) + cos (\frac{π}{4})

Rewrite using trig identities:

sin (\frac{7 π}{6}) = - \frac{1}{2}

Use the following trivial identity:

cos (\frac{π}{4}) = \frac{2}{2}

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

Simplify

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

= \frac{1 + 2}{2}

arcsin (\frac{2}{3})

36 sin (4 8^{\circ})

\frac{2 cos ( 0.1 ) - 2}{0.1}

arctan (\frac{26}{35})

cos (- \frac{95 π}{4})

What is the value of sin(-(7pi)/6)+cos(-pi/4) ?
The value of sin(-(7pi)/6)+cos(-pi/4) is (1+sqrt(2))/2