What is the general solution for cos(2B)= 21/35 ?

The general solution for cos(2B)= 21/35 is B=(0.92729…)/2+pin,B=pi-(0.92729…)/2+pin

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cos(2B)= 21/35

cos (2 B) = \frac{21}{35}

B = \frac{0.92729 \dots}{2} + πn, B = π - \frac{0.92729 \dots}{2} + πn

Degrees

B = 26.56505 \dots^{\circ} + 18 0^{\circ} n, B = 153.43494 \dots^{\circ} + 18 0^{\circ} n

Solution steps

cos (2 B) = \frac{21}{35}

Cancel the common factor:

7

cos (2 B) = \frac{3}{5}

Apply trig inverse properties

cos (2 B) = \frac{3}{5}

General solutions for

cos (2 B) = \frac{3}{5}

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

2 B = arccos (\frac{3}{5}) + 2 πn, 2 B = 2 π - arccos (\frac{3}{5}) + 2 πn

2 B = arccos (\frac{3}{5}) + 2 πn, 2 B = 2 π - arccos (\frac{3}{5}) + 2 πn

Solve

2 B = arccos (\frac{3}{5}) + 2 πn : B = \frac{arccos ( \frac{3}{5} )}{2} + πn

2 B = arccos (\frac{3}{5}) + 2 πn

Divide both sides by

2

2 B = arccos (\frac{3}{5}) + 2 πn

Divide both sides by

2

\frac{2 B}{2} = \frac{arccos ( \frac{3}{5} )}{2} + \frac{2 πn}{2}

Simplify

B = \frac{arccos ( \frac{3}{5} )}{2} + πn

B = \frac{arccos ( \frac{3}{5} )}{2} + πn

Solve

2 B = 2 π - arccos (\frac{3}{5}) + 2 πn : B = π - \frac{arccos ( \frac{3}{5} )}{2} + πn

2 B = 2 π - arccos (\frac{3}{5}) + 2 πn

Divide both sides by

2

2 B = 2 π - arccos (\frac{3}{5}) + 2 πn

Divide both sides by

2

\frac{2 B}{2} = \frac{2 π}{2} - \frac{arccos ( \frac{3}{5} )}{2} + \frac{2 πn}{2}

Simplify

B = π - \frac{arccos ( \frac{3}{5} )}{2} + πn

B = π - \frac{arccos ( \frac{3}{5} )}{2} + πn

B = \frac{arccos ( \frac{3}{5} )}{2} + πn, B = π - \frac{arccos ( \frac{3}{5} )}{2} + πn

Show solutions in decimal form

B = \frac{0.92729 \dots}{2} + πn, B = π - \frac{0.92729 \dots}{2} + πn

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

x, arcsin (x + y) = 0

1 + cos (π x) = sin (π x)

sin (x - 1 5^{\circ}) = cos (2 0^{\circ} + x)

15 sin^{2} (x) - 17 sin (x) + 4 = 0

What is the general solution for cos(2B)= 21/35 ?
The general solution for cos(2B)= 21/35 is B=(0.92729…)/2+pin,B=pi-(0.92729…)/2+pin