What is the general solution for 376=80*24.7*cos(x) ?

The general solution for 376=80*24.7*cos(x) is x=1.37934…+2pin,x=2pi-1.37934…+2pin

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376=8024.7cos(x)

376 = 80 \cdot 24.7 \cdot cos (x)

x = 1.37934 \dots + 2 πn, x = 2 π - 1.37934 \dots + 2 πn

Degrees

x = 79.03067 \dots^{\circ} + 36 0^{\circ} n, x = 280.96932 \dots^{\circ} + 36 0^{\circ} n

Solution steps

376 = 80 \cdot 24.7 cos (x)

Switch sides

80 \cdot 24.7 cos (x) = 376

Divide both sides by

1976

80 \cdot 24.7 cos (x) = 376

Divide both sides by

1976

\frac{80 \cdot 24.7 cos ( x )}{1976} = \frac{376}{1976}

Simplify

cos (x) = \frac{47}{247}

cos (x) = \frac{47}{247}

Apply trig inverse properties

cos (x) = \frac{47}{247}

General solutions for

cos (x) = \frac{47}{247}

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

x = arccos (\frac{47}{247}) + 2 πn, x = 2 π - arccos (\frac{47}{247}) + 2 πn

x = arccos (\frac{47}{247}) + 2 πn, x = 2 π - arccos (\frac{47}{247}) + 2 πn

Show solutions in decimal form

x = 1.37934 \dots + 2 πn, x = 2 π - 1.37934 \dots + 2 πn

What is the general solution for 376=80*24.7*cos(x) ?
The general solution for 376=80*24.7*cos(x) is x=1.37934…+2pin,x=2pi-1.37934…+2pin