What is the general solution for cos(2t)-cos(t)=0.5 ?

The general solution for cos(2t)-cos(t)=0.5 is t=2.28020…+2pin,t=-2.28020…+2pin

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cos(2t)-cos(t)=0.5

cos (2 t) - cos (t) = 0.5

t = 2.28020 \dots + 2 πn, t = - 2.28020 \dots + 2 πn

Solution steps

cos (2 t) - cos (t) = 0.5

Subtract

0.5

from both sides

cos (2 t) - cos (t) - 0.5 = 0

Rewrite using trig identities

- 1.5 - cos (t) + 2 cos^{2} (t) = 0

Solve by substitution

cos (t) = \frac{1 + 13}{4}, cos (t) = \frac{1 - 13}{4}

cos (t) = \frac{1 + 13}{4} :

No Solution

cos (t) = \frac{1 - 13}{4} : t = arccos (\frac{1 - 13}{4}) + 2 πn, t = - arccos (\frac{1 - 13}{4}) + 2 πn

Combine all the solutions

t = arccos (\frac{1 - 13}{4}) + 2 πn, t = - arccos (\frac{1 - 13}{4}) + 2 πn

Show solutions in decimal form

t = 2.28020 \dots + 2 πn, t = - 2.28020 \dots + 2 πn

0 = - 6 csc (x) cot (x)

0.08 = 0.12 cos^{2} (3.922 t)

\frac{15}{sin ( 3 2 ^{\circ} )} = \frac{12}{sin ( b )}

\frac{sin ( x )}{25} = \frac{sin ( 12 5 ^{\circ} )}{165.6}

2 cos (3 θ) - 1 = 0

What is the general solution for cos(2t)-cos(t)=0.5 ?
The general solution for cos(2t)-cos(t)=0.5 is t=2.28020…+2pin,t=-2.28020…+2pin