What is the general solution for tan(x-60)=-1.26 ?

The general solution for tan(x-60)=-1.26 is x=-0.89993…+180n+60

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tan(x-60)=-1.26

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

x = - 0.89993 \dots + 18 0^{\circ} n + 6 0^{\circ}

Radians

x = - 0.89993 \dots + \frac{π}{3} + πn

Solution steps

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

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}

Show solutions in decimal form

x = - 0.89993 \dots + 18 0^{\circ} n + 6 0^{\circ}

sin (t) = \frac{7}{9}

3 sec (x) = - 5

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

tan (3 x + \frac{3 π}{4}) - 1 = 0

sin (10 5^{\circ}) sin (x^{\circ}) = \frac{3 + 2}{4}

What is the general solution for tan(x-60)=-1.26 ?
The general solution for tan(x-60)=-1.26 is x=-0.89993…+180n+60