What is the value of sin^2((5pi)/6)+cos^2((5pi)/6) ?

The value of sin^2((5pi)/6)+cos^2((5pi)/6) is 1

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sin^2((5pi)/6)+cos^2((5pi)/6)

sin^{2} (\frac{5 π}{6}) + cos^{2} (\frac{5 π}{6})

1

Solution steps

sin^{2} (\frac{5 π}{6}) + cos^{2} (\frac{5 π}{6})

Use the following trivial identity:

sin (\frac{5 π}{6}) = \frac{1}{2}

Use the following trivial identity:

cos (\frac{5 π}{6}) = - \frac{3}{2}

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

Simplify

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

= 1

arccos (\frac{12}{20})

9 cos (4 5^{\circ})

arccos (0.304563)

arctan (- \frac{2 3}{2})

cos (17 8^{\circ})

What is the value of sin^2((5pi)/6)+cos^2((5pi)/6) ?
The value of sin^2((5pi)/6)+cos^2((5pi)/6) is 1