What is the value of (-sin^2(33)-cos^2(33))/(sqrt(5)) ?

The value of (-sin^2(33)-cos^2(33))/(sqrt(5)) is -(sqrt(5))/5

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(-sin^2(33)-cos^2(33))/(sqrt(5))

\frac{- sin ^{2} ( 3 3 ^{\circ} ) - cos ^{2} ( 3 3 ^{\circ} )}{5}

- \frac{5}{5}

Decimal Notation

- 0.4472135955

Solution steps

\frac{- sin ^{2} ( 3 3 ^{\circ} ) - cos ^{2} ( 3 3 ^{\circ} )}{5}

Simplify

= \frac{5 ( - sin ^{2} ( 3 3 ^{\circ} ) - cos ^{2} ( 3 3 ^{\circ} ) )}{5}

Rewrite using trig identities:

- cos^{2} (3 3^{\circ}) - sin^{2} (3 3^{\circ}) = - 1

- cos^{2} (3 3^{\circ}) - sin^{2} (3 3^{\circ})

Use the Pythagorean identity:

cos^{2} (x) + sin^{2} (x) = 1

- cos^{2} (x) - sin^{2} (x) = - 1

= - 1

= \frac{5 ( - 1 )}{5}

Simplify

= - \frac{5}{5}

sin (3 6^{\circ}) \cdot 5

cos (4 (- \frac{π}{6}))

cot (\frac{- 7 π}{6})

40 sin (5 0^{\circ})

sin (\frac{2}{3}) π

What is the value of (-sin^2(33)-cos^2(33))/(sqrt(5)) ?
The value of (-sin^2(33)-cos^2(33))/(sqrt(5)) is -(sqrt(5))/5