What is the general solution for 500=538.5cos(x-10) ?

The general solution for 500=538.5cos(x-10) is x=0.38042…+360n+10,x=360-0.38042…+360n+10

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500=538.5cos(x-10)

500 = 538.5 cos (x - 1 0^{\circ})

x = 0.38042 \dots + 36 0^{\circ} n + 1 0^{\circ}, x = 36 0^{\circ} - 0.38042 \dots + 36 0^{\circ} n + 1 0^{\circ}

Solution steps

500 = 538.5 cos (x - 1 0^{\circ})

Switch sides

538.5 cos (x - 1 0^{\circ}) = 500

Multiply both sides by

10

5385 cos (x - 1 0^{\circ}) = 5000

Divide both sides by

5385

cos (x - 1 0^{\circ}) = \frac{1000}{1077}

Apply trig inverse properties

x - 1 0^{\circ} = arccos (\frac{1000}{1077}) + 36 0^{\circ} n, x - 1 0^{\circ} = 36 0^{\circ} - arccos (\frac{1000}{1077}) + 36 0^{\circ} n

Solve

x - 1 0^{\circ} = arccos (\frac{1000}{1077}) + 36 0^{\circ} n : x = arccos (\frac{1000}{1077}) + 36 0^{\circ} n + 1 0^{\circ}

Solve

x - 1 0^{\circ} = 36 0^{\circ} - arccos (\frac{1000}{1077}) + 36 0^{\circ} n : x = 36 0^{\circ} - arccos (\frac{1000}{1077}) + 36 0^{\circ} n + 1 0^{\circ}

x = arccos (\frac{1000}{1077}) + 36 0^{\circ} n + 1 0^{\circ}, x = 36 0^{\circ} - arccos (\frac{1000}{1077}) + 36 0^{\circ} n + 1 0^{\circ}

Show solutions in decimal form

x = 0.38042 \dots + 36 0^{\circ} n + 1 0^{\circ}, x = 36 0^{\circ} - 0.38042 \dots + 36 0^{\circ} n + 1 0^{\circ}

- 2 cos^{2} (x) = 3 (sin (x) - 1)

cos (x) tan (x) = sin (2 x)

2 ∣ sin (4 θ) ∣ = 0

250 sin (7 5^{\circ}) = 393.19 sin (4 5^{\circ} - θ)

tan (θ) = \frac{6}{6.71}

What is the general solution for 500=538.5cos(x-10) ?
The general solution for 500=538.5cos(x-10) is x=0.38042…+360n+10,x=360-0.38042…+360n+10