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Phổ biến >

csc(2x+3)= 5/4

Lời Giải

csc (2 x + 3^{\circ}) = \frac{5}{4}

Lời Giải

x = 18 0^{\circ} n - 1. 5^{\circ} + \frac{0.92729 \dots}{2}, x = 18 0^{\circ} n + 9 0^{\circ} - 1. 5^{\circ} - \frac{0.92729 \dots}{2}

+1

radian

x = - \frac{π}{120} + \frac{0.92729 \dots}{2} + πn, x = \frac{π}{2} - \frac{π}{120} - \frac{0.92729 \dots}{2} + πn

Các bước giải pháp

csc (2 x + 3^{\circ}) = \frac{5}{4}

Áp dụng tính chất nghịch đảo lượng giác

csc (2 x + 3^{\circ}) = \frac{5}{4}

Các lời giải chung cho

csc (2 x + 3^{\circ}) = \frac{5}{4}

csc (x) = a \Rightarrow x = arccsc (a) + 36 0^{\circ} n, x = 18 0^{\circ} - arccsc (a) + 36 0^{\circ} n

2 x + 3^{\circ} = arccsc (\frac{5}{4}) + 36 0^{\circ} n, 2 x + 3^{\circ} = 18 0^{\circ} - arccsc (\frac{5}{4}) + 36 0^{\circ} n

2 x + 3^{\circ} = arccsc (\frac{5}{4}) + 36 0^{\circ} n, 2 x + 3^{\circ} = 18 0^{\circ} - arccsc (\frac{5}{4}) + 36 0^{\circ} n

Giải

2 x + 3^{\circ} = arccsc (\frac{5}{4}) + 36 0^{\circ} n : x = 18 0^{\circ} n - 1. 5^{\circ} + \frac{arccsc ( \frac{5}{4} )}{2}

2 x + 3^{\circ} = arccsc (\frac{5}{4}) + 36 0^{\circ} n

Di chuyển

3^{\circ}

sang vế phải

2 x + 3^{\circ} = arccsc (\frac{5}{4}) + 36 0^{\circ} n

Trừ

3^{\circ}

cho cả hai bên

2 x + 3^{\circ} - 3^{\circ} = arccsc (\frac{5}{4}) + 36 0^{\circ} n - 3^{\circ}

Rút gọn

2 x = arccsc (\frac{5}{4}) + 36 0^{\circ} n - 3^{\circ}

2 x = arccsc (\frac{5}{4}) + 36 0^{\circ} n - 3^{\circ}

Chia cả hai vế cho

2

2 x = arccsc (\frac{5}{4}) + 36 0^{\circ} n - 3^{\circ}

Chia cả hai vế cho

2

\frac{2 x}{2} = \frac{arccsc ( \frac{5}{4} )}{2} + \frac{36 0 ^{\circ} n}{2} - \frac{3 ^{\circ}}{2}

Rút gọn

\frac{2 x}{2} = \frac{arccsc ( \frac{5}{4} )}{2} + \frac{36 0 ^{\circ} n}{2} - \frac{3 ^{\circ}}{2}

Rút gọn

\frac{2 x}{2} : x

\frac{2 x}{2}

Chia các số:

\frac{2}{2} = 1

= x

Rút gọn

\frac{arccsc ( \frac{5}{4} )}{2} + \frac{36 0 ^{\circ} n}{2} - \frac{3 ^{\circ}}{2} : 18 0^{\circ} n - 1. 5^{\circ} + \frac{arccsc ( \frac{5}{4} )}{2}

\frac{arccsc ( \frac{5}{4} )}{2} + \frac{36 0 ^{\circ} n}{2} - \frac{3 ^{\circ}}{2}

Nhóm các thuật ngữ

= \frac{36 0 ^{\circ} n}{2} - \frac{3 ^{\circ}}{2} + \frac{arccsc ( \frac{5}{4} )}{2}

\frac{36 0 ^{\circ} n}{2} = 18 0^{\circ} n

\frac{36 0 ^{\circ} n}{2}

Chia các số:

\frac{2}{2} = 1

= 18 0^{\circ} n

\frac{3 ^{\circ}}{2} = 1. 5^{\circ}

\frac{3 ^{\circ}}{2}

Áp dụng quy tắc phân số:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{18 0 ^{\circ}}{60 \cdot 2}

Nhân các số:

60 \cdot 2 = 120

= 1. 5^{\circ}

= 18 0^{\circ} n - 1. 5^{\circ} + \frac{arccsc ( \frac{5}{4} )}{2}

x = 18 0^{\circ} n - 1. 5^{\circ} + \frac{arccsc ( \frac{5}{4} )}{2}

x = 18 0^{\circ} n - 1. 5^{\circ} + \frac{arccsc ( \frac{5}{4} )}{2}

x = 18 0^{\circ} n - 1. 5^{\circ} + \frac{arccsc ( \frac{5}{4} )}{2}

Giải

2 x + 3^{\circ} = 18 0^{\circ} - arccsc (\frac{5}{4}) + 36 0^{\circ} n : x = 18 0^{\circ} n + 9 0^{\circ} - 1. 5^{\circ} - \frac{arccsc ( \frac{5}{4} )}{2}

2 x + 3^{\circ} = 18 0^{\circ} - arccsc (\frac{5}{4}) + 36 0^{\circ} n

Di chuyển

3^{\circ}

sang vế phải

2 x + 3^{\circ} = 18 0^{\circ} - arccsc (\frac{5}{4}) + 36 0^{\circ} n

Trừ

3^{\circ}

cho cả hai bên

2 x + 3^{\circ} - 3^{\circ} = 18 0^{\circ} - arccsc (\frac{5}{4}) + 36 0^{\circ} n - 3^{\circ}

Rút gọn

2 x = 18 0^{\circ} - arccsc (\frac{5}{4}) + 36 0^{\circ} n - 3^{\circ}

2 x = 18 0^{\circ} - arccsc (\frac{5}{4}) + 36 0^{\circ} n - 3^{\circ}

Chia cả hai vế cho

2

2 x = 18 0^{\circ} - arccsc (\frac{5}{4}) + 36 0^{\circ} n - 3^{\circ}

Chia cả hai vế cho

2

\frac{2 x}{2} = 9 0^{\circ} - \frac{arccsc ( \frac{5}{4} )}{2} + \frac{36 0 ^{\circ} n}{2} - \frac{3 ^{\circ}}{2}

Rút gọn

\frac{2 x}{2} = 9 0^{\circ} - \frac{arccsc ( \frac{5}{4} )}{2} + \frac{36 0 ^{\circ} n}{2} - \frac{3 ^{\circ}}{2}

Rút gọn

\frac{2 x}{2} : x

\frac{2 x}{2}

Chia các số:

\frac{2}{2} = 1

= x

Rút gọn

9 0^{\circ} - \frac{arccsc ( \frac{5}{4} )}{2} + \frac{36 0 ^{\circ} n}{2} - \frac{3 ^{\circ}}{2} : 18 0^{\circ} n + 9 0^{\circ} - 1. 5^{\circ} - \frac{arccsc ( \frac{5}{4} )}{2}

9 0^{\circ} - \frac{arccsc ( \frac{5}{4} )}{2} + \frac{36 0 ^{\circ} n}{2} - \frac{3 ^{\circ}}{2}

Nhóm các thuật ngữ

= 9 0^{\circ} + \frac{36 0 ^{\circ} n}{2} - \frac{3 ^{\circ}}{2} - \frac{arccsc ( \frac{5}{4} )}{2}

\frac{36 0 ^{\circ} n}{2} = 18 0^{\circ} n

\frac{36 0 ^{\circ} n}{2}

Chia các số:

\frac{2}{2} = 1

= 18 0^{\circ} n

\frac{3 ^{\circ}}{2} = 1. 5^{\circ}

\frac{3 ^{\circ}}{2}

Áp dụng quy tắc phân số:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{18 0 ^{\circ}}{60 \cdot 2}

Nhân các số:

60 \cdot 2 = 120

= 1. 5^{\circ}

= 9 0^{\circ} + 18 0^{\circ} n - 1. 5^{\circ} - \frac{arccsc ( \frac{5}{4} )}{2}

Nhóm các thuật ngữ

= 18 0^{\circ} n + 9 0^{\circ} - 1. 5^{\circ} - \frac{arccsc ( \frac{5}{4} )}{2}

x = 18 0^{\circ} n + 9 0^{\circ} - 1. 5^{\circ} - \frac{arccsc ( \frac{5}{4} )}{2}

x = 18 0^{\circ} n + 9 0^{\circ} - 1. 5^{\circ} - \frac{arccsc ( \frac{5}{4} )}{2}

x = 18 0^{\circ} n + 9 0^{\circ} - 1. 5^{\circ} - \frac{arccsc ( \frac{5}{4} )}{2}

x = 18 0^{\circ} n - 1. 5^{\circ} + \frac{arccsc ( \frac{5}{4} )}{2}, x = 18 0^{\circ} n + 9 0^{\circ} - 1. 5^{\circ} - \frac{arccsc ( \frac{5}{4} )}{2}

Hiển thị các lời giải ở dạng thập phân

x = 18 0^{\circ} n - 1. 5^{\circ} + \frac{0.92729 \dots}{2}, x = 18 0^{\circ} n + 9 0^{\circ} - 1. 5^{\circ} - \frac{0.92729 \dots}{2}

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

cos(x)=0.998482

cos (x) = 0.998482

3sin(2x)-sin(x)=0

3 sin (2 x) - sin (x) = 0

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