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人気のある三角関数 >

sec(x)sin(x)-3sin(x)=0,0<= x<= 360

解

sec (x) sin (x) - 3 sin (x) = 0, 0 \leq x \leq 36 0^{\circ}

解

x = 0, x = 18 0^{\circ}, x = 36 0^{\circ}, x = 1.23095 \dots, x = 36 0^{\circ} - 1.23095 \dots

+1

ラジアン

x = 0, x = π, x = 2 π, x = 1.23095 \dots, x = 2 π - 1.23095 \dots

解答ステップ

sec (x) sin (x) - 3 sin (x) = 0, 0 \leq x \leq 36 0^{\circ}

因数

sec (x) sin (x) - 3 sin (x) : sin (x) (sec (x) - 3)

sec (x) sin (x) - 3 sin (x)

共通項をくくり出す

sin (x)

= sin (x) (sec (x) - 3)

sin (x) (sec (x) - 3) = 0

各部分を別個に解く

sin (x) = 0 or sec (x) - 3 = 0

sin (x) = 0, 0 \leq x \leq 36 0^{\circ} : x = 0, x = 18 0^{\circ}, x = 36 0^{\circ}

sin (x) = 0, 0 \leq x \leq 36 0^{\circ}

以下の一般解

sin (x) = 0

sin (x)

36 0^{\circ} n

循環を含む周期性テーブル:

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}

x = 0 + 36 0^{\circ} n, x = 18 0^{\circ} + 36 0^{\circ} n

x = 0 + 36 0^{\circ} n, x = 18 0^{\circ} + 36 0^{\circ} n

解く

x = 0 + 36 0^{\circ} n : x = 36 0^{\circ} n

x = 0 + 36 0^{\circ} n

0 + 36 0^{\circ} n = 36 0^{\circ} n

x = 36 0^{\circ} n

x = 36 0^{\circ} n, x = 18 0^{\circ} + 36 0^{\circ} n

範囲の解答

0 \leq x \leq 36 0^{\circ}

x = 0, x = 18 0^{\circ}, x = 36 0^{\circ}

sec (x) - 3 = 0, 0 \leq x \leq 36 0^{\circ} : x = arcsec (3), x = 36 0^{\circ} - arcsec (3)

sec (x) - 3 = 0, 0 \leq x \leq 36 0^{\circ}

3

を右側に移動します

sec (x) - 3 = 0

両辺に

3

を足す

sec (x) - 3 + 3 = 0 + 3

簡素化

sec (x) = 3

sec (x) = 3

三角関数の逆数プロパティを適用する

sec (x) = 3

以下の一般解

sec (x) = 3

sec (x) = a \Rightarrow x = arcsec (a) + 36 0^{\circ} n, x = 36 0^{\circ} - arcsec (a) + 36 0^{\circ} n

x = arcsec (3) + 36 0^{\circ} n, x = 36 0^{\circ} - arcsec (3) + 36 0^{\circ} n

x = arcsec (3) + 36 0^{\circ} n, x = 36 0^{\circ} - arcsec (3) + 36 0^{\circ} n

範囲の解答

0 \leq x \leq 36 0^{\circ}

x = arcsec (3), x = 36 0^{\circ} - arcsec (3)

すべての解を組み合わせる

x = 0, x = 18 0^{\circ}, x = 36 0^{\circ}, x = arcsec (3), x = 36 0^{\circ} - arcsec (3)

10進法形式で解を証明する

x = 0, x = 18 0^{\circ}, x = 36 0^{\circ}, x = 1.23095 \dots, x = 36 0^{\circ} - 1.23095 \dots

グラフ

人気の例

4 sin (\frac{x}{2}) - 1 = 1

3 sec (θ) + 6 = 0

sin(x)-sin(x)*cos(x)=0,0<= x<= 2pi

sin (x) - sin (x) \cdot cos (x) = 0, 0 \leq x \leq 2 π

8sin(x)+6cos(x)=8

8 sin (x) + 6 cos (x) = 8

2tan^2(x)-5tan(x)+3=0

2 tan^{2} (x) - 5 tan (x) + 3 = 0