What is the general solution for tan(3r+2)=45 ?

The general solution for tan(3r+2)=45 is r=(0.66577…)/3+(180n)/3-2/3

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tan(3r+2)=45

tan (3 r + 2) = 4 5^{\circ}

r = \frac{0.66577 \dots}{3} + \frac{18 0 ^{\circ} n}{3} - \frac{2}{3}

Radians

r = \frac{0.66577 \dots}{3} - \frac{2}{3} + \frac{π}{3} n

Solution steps

tan (3 r + 2) = 4 5^{\circ}

Apply trig inverse properties

tan (3 r + 2) = 4 5^{\circ}

General solutions for

tan (3 r + 2) = 4 5^{\circ}

tan (x) = a \Rightarrow x = arctan (a) + 18 0^{\circ} n

3 r + 2 = arctan (4 5^{\circ}) + 18 0^{\circ} n

3 r + 2 = arctan (4 5^{\circ}) + 18 0^{\circ} n

Solve

3 r + 2 = arctan (4 5^{\circ}) + 18 0^{\circ} n : r = \frac{arctan ( 4 5 ^{\circ} )}{3} + \frac{18 0 ^{\circ} n}{3} - \frac{2}{3}

3 r + 2 = arctan (4 5^{\circ}) + 18 0^{\circ} n

Move

2

to the right side

3 r + 2 = arctan (4 5^{\circ}) + 18 0^{\circ} n

Subtract

2

from both sides

3 r + 2 - 2 = arctan (4 5^{\circ}) + 18 0^{\circ} n - 2

Simplify

3 r = arctan (4 5^{\circ}) + 18 0^{\circ} n - 2

3 r = arctan (4 5^{\circ}) + 18 0^{\circ} n - 2

Divide both sides by

3

3 r = arctan (4 5^{\circ}) + 18 0^{\circ} n - 2

Divide both sides by

3

\frac{3 r}{3} = \frac{arctan ( 4 5 ^{\circ} )}{3} + \frac{18 0 ^{\circ} n}{3} - \frac{2}{3}

Simplify

r = \frac{arctan ( 4 5 ^{\circ} )}{3} + \frac{18 0 ^{\circ} n}{3} - \frac{2}{3}

r = \frac{arctan ( 4 5 ^{\circ} )}{3} + \frac{18 0 ^{\circ} n}{3} - \frac{2}{3}

r = \frac{arctan ( 4 5 ^{\circ} )}{3} + \frac{18 0 ^{\circ} n}{3} - \frac{2}{3}

Show solutions in decimal form

r = \frac{0.66577 \dots}{3} + \frac{18 0 ^{\circ} n}{3} - \frac{2}{3}

8 sin^{3} (x) - 6 sin (x) + 1 = 0

cos^{2} (z) = \frac{3}{2}

sin (x) + 2 cos (x) = - sin (3 x)

cos (x) = 0.85

4 sin^{2} (x) - 1 = 0, 0 \leq x \leq 2 π

What is the general solution for tan(3r+2)=45 ?
The general solution for tan(3r+2)=45 is r=(0.66577…)/3+(180n)/3-2/3