What is the value of (sin^2(pi)-4cos^2(pi))/pi ?

The value of (sin^2(pi)-4cos^2(pi))/pi is -4/pi

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(sin^2(pi)-4cos^2(pi))/pi

\frac{sin ^{2} ( π ) - 4 cos ^{2} ( π )}{π}

- \frac{4}{π}

Decimal Notation

- 1.27323 \dots

Solution steps

\frac{sin ^{2} ( π ) - 4 cos ^{2} ( π )}{π}

Use the following trivial identity:

sin (π) = 0

sin (π)

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= 0

Use the following trivial identity:

cos (π) = (- 1)

cos (π)

cos (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= (- 1)

= \frac{0 ^{2} - 4 ( - 1 ) ^{2}}{π}

Simplify

\frac{0 ^{2} - 4 ( - 1 ) ^{2}}{π} : - \frac{4}{π}

\frac{0 ^{2} - 4 ( - 1 ) ^{2}}{π}

Apply rule

0^{a} = 0

0^{2} = 0

= \frac{0 - ( - 1 ) ^{2} \cdot 4}{π}

0 - 4 (- 1)^{2} = - 4

0 - 4 (- 1)^{2}

4 (- 1)^{2} = 4

4 (- 1)^{2}

(- 1)^{2} = 1

(- 1)^{2}

Apply exponent rule:

(- a)^{n} = a^{n},

n

is even

(- 1)^{2} = 1^{2}

= 1^{2}

Apply rule

1^{a} = 1

= 1

= 4 \cdot 1

Multiply the numbers:

4 \cdot 1 = 4

= 4

= 0 - 4

Subtract the numbers:

0 - 4 = - 4

= - 4

= \frac{- 4}{π}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{4}{π}

= - \frac{4}{π}

\frac{4.8}{sin ( 5 4 ^{\circ} )}

500 \cdot sin (3 0^{\circ})

30 \cdot cos (3 7^{\circ})

5 tan^{2} (4 5^{\circ}) + 2 sec^{2} (4 5^{\circ})

4 - sin (3)

What is the value of (sin^2(pi)-4cos^2(pi))/pi ?
The value of (sin^2(pi)-4cos^2(pi))/pi is -4/pi