What is the general solution for tan(x-60)=-1.26,0<= x<= 360 ?

The general solution for tan(x-60)=-1.26,0<= x<= 360 is x=(180-3*0.89993…)/3 ,x=(-3*0.89993…+720)/3

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tan(x-60)=-1.26,0<= x<= 360

tan (x - 6 0^{\circ}) = - 1.26, 0^{\circ} \leq x \leq 36 0^{\circ}

x = \frac{18 0 ^{\circ} - 3 \cdot 0.89993 \dots}{3}, x = \frac{- 3 \cdot 0.89993 \dots + 72 0 ^{\circ}}{3}

Radians

x = \frac{π - 3 \cdot 0.89993 \dots}{3}, x = \frac{- 3 \cdot 0.89993 \dots + 4 π}{3}

Solution steps

tan (x - 6 0^{\circ}) = - 1.26, 0^{\circ} \leq x \leq 36 0^{\circ}

Apply trig inverse properties

tan (x - 6 0^{\circ}) = - 1.26

General solutions for

tan (x - 6 0^{\circ}) = - 1.26

tan (x) = - a \Rightarrow x = arctan (- a) + 18 0^{\circ} n

x - 6 0^{\circ} = arctan (- 1.26) + 18 0^{\circ} n

x - 6 0^{\circ} = arctan (- 1.26) + 18 0^{\circ} n

Solve

x - 6 0^{\circ} = arctan (- 1.26) + 18 0^{\circ} n : x = - arctan (\frac{63}{50}) + 18 0^{\circ} n + 6 0^{\circ}

x - 6 0^{\circ} = arctan (- 1.26) + 18 0^{\circ} n

Simplify

arctan (- 1.26) + 18 0^{\circ} n : - arctan (\frac{63}{50}) + 18 0^{\circ} n

arctan (- 1.26) + 18 0^{\circ} n

arctan (- 1.26) = - arctan (\frac{63}{50})

arctan (- 1.26)

= arctan (- \frac{63}{50})

Use the following property:

arctan (- x) = - arctan (x)

arctan (- \frac{63}{50}) = - arctan (\frac{63}{50})

= - arctan (\frac{63}{50})

= - arctan (\frac{63}{50}) + 18 0^{\circ} n

x - 6 0^{\circ} = - arctan (\frac{63}{50}) + 18 0^{\circ} n

Move

6 0^{\circ}

to the right side

x - 6 0^{\circ} = - arctan (\frac{63}{50}) + 18 0^{\circ} n

Add

6 0^{\circ}

to both sides

x - 6 0^{\circ} + 6 0^{\circ} = - arctan (\frac{63}{50}) + 18 0^{\circ} n + 6 0^{\circ}

Simplify

x = - arctan (\frac{63}{50}) + 18 0^{\circ} n + 6 0^{\circ}

x = - arctan (\frac{63}{50}) + 18 0^{\circ} n + 6 0^{\circ}

x = - arctan (\frac{63}{50}) + 18 0^{\circ} n + 6 0^{\circ}

Solutions for the range

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

x = \frac{18 0 ^{\circ} - 3 arctan ( \frac{63}{50} )}{3}, x = \frac{- 3 arctan ( \frac{63}{50} ) + 72 0 ^{\circ}}{3}

Show solutions in decimal form

x = \frac{18 0 ^{\circ} - 3 \cdot 0.89993 \dots}{3}, x = \frac{- 3 \cdot 0.89993 \dots + 72 0 ^{\circ}}{3}

0 = 1.5961 \cdot cos (x) + 0.0422 \cdot cos (2 \cdot x)

6 cos (7 θ) = 0

csc^{2} (θ) = 3 cot (θ) + 5

sin^{2} (x) - 2 sin (x) = 0, 0 \leq x < 2 π

cos (2 x) = \frac{( 5 k - 8 )}{5}

What is the general solution for tan(x-60)=-1.26,0<= x<= 360 ?
The general solution for tan(x-60)=-1.26,0<= x<= 360 is x=(180-3*0.89993…)/3 ,x=(-3*0.89993…+720)/3