What is the general solution for cos(6x)=1,0<= x<= pi/2 ?

The general solution for cos(6x)=1,0<= x<= pi/2 is x=0,x= pi/3

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cos(6x)=1,0<= x<= pi/2

cos (6 x) = 1, 0 \leq x \leq \frac{π}{2}

x = 0, x = \frac{π}{3}

Degrees

x = 0^{\circ}, x = 6 0^{\circ}

Solution steps

cos (6 x) = 1, 0 \leq x \leq \frac{π}{2}

General solutions for

cos (6 x) = 1

cos (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

6 x = 0 + 2 πn

6 x = 0 + 2 πn

Solve

6 x = 0 + 2 πn : x = \frac{πn}{3}

6 x = 0 + 2 πn

0 + 2 πn = 2 πn

6 x = 2 πn

Divide both sides by

6

6 x = 2 πn

Divide both sides by

6

\frac{6 x}{6} = \frac{2 πn}{6}

Simplify

x = \frac{πn}{3}

x = \frac{πn}{3}

x = \frac{πn}{3}

Solutions for the range

0 \leq x \leq \frac{π}{2}

x = 0, x = \frac{π}{3}

cos^{2} (θ) + 2 cos (θ) - 3 = 0

cos (2 θ) = 11 sin (θ) - 5

4 tan (θ) = 3 + tan (θ)

tan (2 x) + sec (2 x) = 10

so l v e f or a, F = (x^{(\frac{2}{3})}) + (0.9 (3.3 - x^{2})^{\frac{1}{2}}) \cdot sin (a p e x)

What is the general solution for cos(6x)=1,0<= x<= pi/2 ?
The general solution for cos(6x)=1,0<= x<= pi/2 is x=0,x= pi/3