What is the general solution for 1.16cos(θ)+0.532cos(θ)-0.557=0 ?

The general solution for 1.16cos(θ)+0.532cos(θ)-0.557=0 is θ=1.23534…+2pin,θ=2pi-1.23534…+2pin

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1.16cos(θ)+0.532cos(θ)-0.557=0

1.16 cos (θ) + 0.532 cos (θ) - 0.557 = 0

θ = 1.23534 \dots + 2 πn, θ = 2 π - 1.23534 \dots + 2 πn

Degrees

θ = 70.78000 \dots^{\circ} + 36 0^{\circ} n, θ = 289.21999 \dots^{\circ} + 36 0^{\circ} n

Solution steps

1.16 cos (θ) + 0.532 cos (θ) - 0.557 = 0

Simplify

1.16 cos (θ) + 0.532 cos (θ) - 0.557 : 1.692 cos (θ) - 0.557

1.16 cos (θ) + 0.532 cos (θ) - 0.557

Add similar elements:

1.16 cos (θ) + 0.532 cos (θ) = 1.692 cos (θ)

= 1.692 cos (θ) - 0.557

1.692 cos (θ) - 0.557 = 0

Multiply both sides by

1000

1.692 cos (θ) - 0.557 = 0

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere are

3

digits to the right of the decimal point, therefore multiply by

1000

1.692 cos (θ) \cdot 1000 - 0.557 \cdot 1000 = 0 \cdot 1000

Refine

1692 cos (θ) - 557 = 0

1692 cos (θ) - 557 = 0

Move

557

to the right side

1692 cos (θ) - 557 = 0

Add

557

to both sides

1692 cos (θ) - 557 + 557 = 0 + 557

Simplify

1692 cos (θ) = 557

1692 cos (θ) = 557

Divide both sides by

1692

1692 cos (θ) = 557

Divide both sides by

1692

\frac{1692 cos ( θ )}{1692} = \frac{557}{1692}

Simplify

cos (θ) = \frac{557}{1692}

cos (θ) = \frac{557}{1692}

Apply trig inverse properties

cos (θ) = \frac{557}{1692}

General solutions for

cos (θ) = \frac{557}{1692}

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = 2 π - arccos (a) + 2 πn

θ = arccos (\frac{557}{1692}) + 2 πn, θ = 2 π - arccos (\frac{557}{1692}) + 2 πn

θ = arccos (\frac{557}{1692}) + 2 πn, θ = 2 π - arccos (\frac{557}{1692}) + 2 πn

Show solutions in decimal form

θ = 1.23534 \dots + 2 πn, θ = 2 π - 1.23534 \dots + 2 πn

arcsin (6 x) + arcsin (63 x) = - \frac{π}{2}

cos (x) = \frac{1}{2}, 0^{\circ} \leq x \leq 36 0^{\circ}

- 44 sin (2 x) + 42 cos (2 x) = 0

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

cos^{2} (x) = cos (x) - 1

What is the general solution for 1.16cos(θ)+0.532cos(θ)-0.557=0 ?
The general solution for 1.16cos(θ)+0.532cos(θ)-0.557=0 is θ=1.23534…+2pin,θ=2pi-1.23534…+2pin