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人気のある三角関数 >

sin^2(x)= 1/3

解

sin^{2} (x) = \frac{1}{3}

解

x = 0.61547 \dots + 2 πn, x = π - 0.61547 \dots + 2 πn, x = - 0.61547 \dots + 2 πn, x = π + 0.61547 \dots + 2 πn

+1

度

x = 35.26438 \dots^{\circ} + 36 0^{\circ} n, x = 144.73561 \dots^{\circ} + 36 0^{\circ} n, x = - 35.26438 \dots^{\circ} + 36 0^{\circ} n, x = 215.26438 \dots^{\circ} + 36 0^{\circ} n

解答ステップ

sin^{2} (x) = \frac{1}{3}

置換で解く

sin^{2} (x) = \frac{1}{3}

仮定:

sin (x) = u

u^{2} = \frac{1}{3}

u^{2} = \frac{1}{3} : u = \frac{1}{3}, u = - \frac{1}{3}

u^{2} = \frac{1}{3}

x^{2} = f (a)

の場合, 解は

x = f (a), - f (a)

u = \frac{1}{3}, u = - \frac{1}{3}

代用を戻す

u = sin (x)

sin (x) = \frac{1}{3}, sin (x) = - \frac{1}{3}

sin (x) = \frac{1}{3}, sin (x) = - \frac{1}{3}

sin (x) = \frac{1}{3} : x = arcsin (\frac{1}{3}) + 2 πn, x = π - arcsin (\frac{1}{3}) + 2 πn

sin (x) = \frac{1}{3}

三角関数の逆数プロパティを適用する

sin (x) = \frac{1}{3}

以下の一般解

sin (x) = \frac{1}{3}

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

x = arcsin (\frac{1}{3}) + 2 πn, x = π - arcsin (\frac{1}{3}) + 2 πn

x = arcsin (\frac{1}{3}) + 2 πn, x = π - arcsin (\frac{1}{3}) + 2 πn

sin (x) = - \frac{1}{3} : x = arcsin (- \frac{1}{3}) + 2 πn, x = π + arcsin (\frac{1}{3}) + 2 πn

sin (x) = - \frac{1}{3}

三角関数の逆数プロパティを適用する

sin (x) = - \frac{1}{3}

以下の一般解

sin (x) = - \frac{1}{3}

sin (x) = - a \Rightarrow x = arcsin (- a) + 2 πn, x = π + arcsin (a) + 2 πn

x = arcsin (- \frac{1}{3}) + 2 πn, x = π + arcsin (\frac{1}{3}) + 2 πn

x = arcsin (- \frac{1}{3}) + 2 πn, x = π + arcsin (\frac{1}{3}) + 2 πn

すべての解を組み合わせる

x = arcsin (\frac{1}{3}) + 2 πn, x = π - arcsin (\frac{1}{3}) + 2 πn, x = arcsin (- \frac{1}{3}) + 2 πn, x = π + arcsin (\frac{1}{3}) + 2 πn

10進法形式で解を証明する

x = 0.61547 \dots + 2 πn, x = π - 0.61547 \dots + 2 πn, x = - 0.61547 \dots + 2 πn, x = π + 0.61547 \dots + 2 πn

グラフ

人気の例

cos (2 x) = - 0.8

0 = - 4 sin (2 x)

cot(x)+1=0,0<= x<2pi

cot (x) + 1 = 0, 0 \leq x < 2 π

sin(x)=(4.4sin(119))/(12.3)

sin (x) = \frac{4.4 sin ( 11 9 ^{\circ} )}{12.3}

-sec^2(x)=2tan(x)

- sec^{2} (x) = 2 tan (x)