What is the general solution for 55^2=50^2+90^2-2*50*90*cos(x) ?

The general solution for 55^2=50^2+90^2-2*50*90*cos(x) is x=0.57043…+2pin,x=2pi-0.57043…+2pin

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55^2=50^2+90^2-25090*cos(x)

5 5^{2} = 5 0^{2} + 9 0^{2} - 2 \cdot 50 \cdot 90 \cdot cos (x)

x = 0.57043 \dots + 2 πn, x = 2 π - 0.57043 \dots + 2 πn

Solution steps

5 5^{2} = 5 0^{2} + 9 0^{2} - 2 \cdot 50 \cdot 90 cos (x)

Switch sides

5 0^{2} + 9 0^{2} - 2 \cdot 50 \cdot 90 cos (x) = 5 5^{2}

Multiply the numbers:

2 \cdot 50 \cdot 90 = 9000

5 0^{2} + 9 0^{2} - 9000 cos (x) = 5 5^{2}

5 0^{2} = 2500

2500 + 9 0^{2} - 9000 cos (x) = 5 5^{2}

9 0^{2} = 8100

2500 + 8100 - 9000 cos (x) = 5 5^{2}

Add the numbers:

2500 + 8100 = 10600

- 9000 cos (x) + 10600 = 5 5^{2}

5 5^{2} = 3025

- 9000 cos (x) + 10600 = 3025

Move

10600

to the right side

- 9000 cos (x) = - 7575

Divide both sides by

- 9000

cos (x) = \frac{101}{120}

Apply trig inverse properties

x = arccos (\frac{101}{120}) + 2 πn, x = 2 π - arccos (\frac{101}{120}) + 2 πn

Show solutions in decimal form

x = 0.57043 \dots + 2 πn, x = 2 π - 0.57043 \dots + 2 πn

x, z = sin (2 x + y)

7 tan (x) = 23 + tan (x), 0^{\circ} \leq θ \leq 9 0^{\circ}

sin (X) = 1

x, \frac{17}{sin ( x )} = \frac{23}{sin ( 7 5 ^{\circ} )}

3 - 2 cos^{2} (x) = 4 sin^{2} (x)

What is the general solution for 55^2=50^2+90^2-2*50*90*cos(x) ?
The general solution for 55^2=50^2+90^2-2*50*90*cos(x) is x=0.57043…+2pin,x=2pi-0.57043…+2pin