4.1=4.2cos(18t)+3

Solution

4.1 = 4.2 cos (18 t) + 3

t = \frac{1.30580 \dots}{18} + \frac{πn}{9}, t = \frac{π}{9} - \frac{1.30580 \dots}{18} + \frac{πn}{9}

Solution steps

4.1 = 4.2 cos (18 t) + 3

Switch sides

4.2 cos (18 t) + 3 = 4.1

Multiply both sides by

10

42 cos (18 t) + 30 = 41

Move

30

to the right side

42 cos (18 t) = 11

Divide both sides by

42

cos (18 t) = \frac{11}{42}

Apply trig inverse properties

18 t = arccos (\frac{11}{42}) + 2 πn, 18 t = 2 π - arccos (\frac{11}{42}) + 2 πn

Solve

18 t = arccos (\frac{11}{42}) + 2 πn : t = \frac{arccos ( \frac{11}{42} )}{18} + \frac{πn}{9}

Solve

18 t = 2 π - arccos (\frac{11}{42}) + 2 πn : t = \frac{π}{9} - \frac{arccos ( \frac{11}{42} )}{18} + \frac{πn}{9}

t = \frac{arccos ( \frac{11}{42} )}{18} + \frac{πn}{9}, t = \frac{π}{9} - \frac{arccos ( \frac{11}{42} )}{18} + \frac{πn}{9}

Show solutions in decimal form

t = \frac{1.30580 \dots}{18} + \frac{πn}{9}, t = \frac{π}{9} - \frac{1.30580 \dots}{18} + \frac{πn}{9}

4 sin (x) - 13 = 2 cos^{2} (x) - 9

cos (θ) = - \frac{8}{11}

sin (θ) = \frac{3}{12}

cos (x) = \frac{12}{17}

x, (d^{3} + d^{2} + 1) y = cos (3 x)