What is the general solution for sec(3x)-cos(30)=0,(x+35)/5 ?

The general solution for sec(3x)-cos(30)=0,(x+35)/5 is No Solution for x\in\mathbb{R}

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sec(3x)-cos(30)=0,(x+35)/5

sec (3 x) - cos (3 0^{\circ}) = 0, \frac{x + 35}{5}

No Solution for x \in R

Solution steps

sec (3 x) - cos (3 0^{\circ}) = 0, \frac{x + 35}{5}

cos (3 0^{\circ}) = \frac{3}{2}

cos (3 0^{\circ})

Use the following trivial identity:

cos (3 0^{\circ}) = \frac{3}{2}

cos (3 0^{\circ})

cos (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= \frac{3}{2}

= \frac{3}{2}

sec (3 x) - \frac{3}{2} = 0

Move

\frac{3}{2}

to the right side

sec (3 x) - \frac{3}{2} = 0

Add

\frac{3}{2}

to both sides

sec (3 x) - \frac{3}{2} + \frac{3}{2} = 0 + \frac{3}{2}

Simplify

sec (3 x) = \frac{3}{2}

sec (3 x) = \frac{3}{2}

sec (x) \leq - 1 or sec (x) \geq 1

No Solution for x \in R

- 2 sin (x) + 3 = 0

sin (θ) = \frac{4}{5}, cos (θ) = \frac{3}{5}

sec (2 x) + tan (2 x) = 8

cos (θ) = \frac{1}{12}

sin (θ) = - \frac{8}{9}

What is the general solution for sec(3x)-cos(30)=0,(x+35)/5 ?
The general solution for sec(3x)-cos(30)=0,(x+35)/5 is No Solution for x\in\mathbb{R}