What is the general solution for cos(x)= 2400/3200 ?

The general solution for cos(x)= 2400/3200 is x=0.72273…+2pin,x=2pi-0.72273…+2pin

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cos(x)= 2400/3200

cos (x) = \frac{2400}{3200}

x = 0.72273 \dots + 2 πn, x = 2 π - 0.72273 \dots + 2 πn

Degrees

x = 41.40962 \dots^{\circ} + 36 0^{\circ} n, x = 318.59037 \dots^{\circ} + 36 0^{\circ} n

Solution steps

cos (x) = \frac{2400}{3200}

Cancel the common factor:

800

cos (x) = \frac{3}{4}

Apply trig inverse properties

cos (x) = \frac{3}{4}

General solutions for

cos (x) = \frac{3}{4}

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

x = arccos (\frac{3}{4}) + 2 πn, x = 2 π - arccos (\frac{3}{4}) + 2 πn

x = arccos (\frac{3}{4}) + 2 πn, x = 2 π - arccos (\frac{3}{4}) + 2 πn

Show solutions in decimal form

x = 0.72273 \dots + 2 πn, x = 2 π - 0.72273 \dots + 2 πn

- 4 sin (x) = - cos^{2} (x) + 5

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

4 cos^{2} (x) - 4 sin (x) - 5 = 0, 0 \leq x \leq 2 π

x, y = cos (b x + y)

\frac{300}{1 - sin ( θ )} = 400 + 400 sin (θ)

What is the general solution for cos(x)= 2400/3200 ?
The general solution for cos(x)= 2400/3200 is x=0.72273…+2pin,x=2pi-0.72273…+2pin