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20cos^2(15)

Solución

20 cos^{2} (1 5^{\circ})

10 (\frac{3}{2} + 1)

Notación decimal

18.66025 \dots

Pasos de solución

20 cos^{2} (1 5^{\circ})

Re-escribir usando identidades trigonométricas:

cos^{2} (1 5^{\circ}) = \frac{1 + cos ( 3 0 ^{\circ} )}{2}

cos^{2} (1 5^{\circ})

Usar la siguiente identidad:

cos^{2} (θ) = \frac{1 + cos ( 2 θ )}{2}

Utilizar la identidad trigonométrica del ángulo doble

cos (2 θ) = 2 cos^{2} (θ) - 1

Intercambiar lados

2 cos^{2} (θ) - 1 = cos (2 θ)

Sumar

1

a ambos lados

2 sin^{2} (θ) = 1 + cos (2 θ)

Dividir ambos lados entre

2

cos^{2} (θ) = \frac{1 + cos ( 2 θ )}{2}

= \frac{1 + cos ( 2 \cdot 1 5 ^{\circ} )}{2}

Simplificar

= \frac{1 + cos ( 3 0 ^{\circ} )}{2}

= 20 \cdot \frac{1 + cos ( 3 0 ^{\circ} )}{2}

Simplificar

= 10 (cos (3 0^{\circ}) + 1)

Utilizar la siguiente identidad trivial:

cos (3 0^{\circ}) = \frac{3}{2}

cos (3 0^{\circ})

cos (x)

tabla de valores periódicos con

36 0^{\circ} n

intervalos:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= \frac{3}{2}

= 10 (\frac{3}{2} + 1)

arctan (\frac{7.9253}{22.356 - 11.184 - 7.061})

2 sin (1) cos (1)

cos (225 \circ)

\frac{0.72}{sin ( 16. 2 ^{\circ} )}

- (π \cdot 0. 6^{2}) cos (9 0^{\circ} - 5 2^{\circ}) (- 249 e^{- 3 (1.5)})