What is the general solution for 4cos(x)+tan(45)=0.6 ?

The general solution for 4cos(x)+tan(45)=0.6 is x=1.67096…+360n,x=-1.67096…+360n

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4cos(x)+tan(45)=0.6

4 cos (x) + tan (4 5^{\circ}) = 0.6

x = 1.67096 \dots + 36 0^{\circ} n, x = - 1.67096 \dots + 36 0^{\circ} n

Radians

x = 1.67096 \dots + 2 πn, x = - 1.67096 \dots + 2 πn

Solution steps

4 cos (x) + tan (4 5^{\circ}) = 0.6

tan (4 5^{\circ}) = 1

tan (4 5^{\circ})

Use the following trivial identity:

tan (4 5^{\circ}) = 1

tan (4 5^{\circ})

tan (x)

periodicity table with

18 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

= 1

= 1

4 cos (x) + 1 = 0.6

Move

1

to the right side

4 cos (x) + 1 = 0.6

Subtract

1

from both sides

4 cos (x) + 1 - 1 = 0.6 - 1

Simplify

4 cos (x) = - 0.4

4 cos (x) = - 0.4

Divide both sides by

4

4 cos (x) = - 0.4

Divide both sides by

4

\frac{4 cos ( x )}{4} = \frac{- 0.4}{4}

Simplify

\frac{4 cos ( x )}{4} = \frac{- 0.4}{4}

Simplify

\frac{4 cos ( x )}{4} : cos (x)

\frac{4 cos ( x )}{4}

Divide the numbers:

\frac{4}{4} = 1

= cos (x)

Simplify

\frac{- 0.4}{4} : - 0.1

\frac{- 0.4}{4}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{0.4}{4}

Divide the numbers:

\frac{0.4}{4} = 0.1

= - 0.1

cos (x) = - 0.1

cos (x) = - 0.1

cos (x) = - 0.1

Apply trig inverse properties

cos (x) = - 0.1

General solutions for

cos (x) = - 0.1

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

x = arccos (- 0.1) + 36 0^{\circ} n, x = - arccos (- 0.1) + 36 0^{\circ} n

x = arccos (- 0.1) + 36 0^{\circ} n, x = - arccos (- 0.1) + 36 0^{\circ} n

Show solutions in decimal form

x = 1.67096 \dots + 36 0^{\circ} n, x = - 1.67096 \dots + 36 0^{\circ} n

What is the general solution for 4cos(x)+tan(45)=0.6 ?
The general solution for 4cos(x)+tan(45)=0.6 is x=1.67096…+360n,x=-1.67096…+360n