What is the general solution for 1715/70 =tan(45+θ/2) ?

The general solution for 1715/70 =tan(45+θ/2) is θ=2*1.53000…+360n-90

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1715/70 =tan(45+θ/2)

\frac{1715}{70} = tan (4 5^{\circ} + \frac{θ}{2})

θ = 2 \cdot 1.53000 \dots + 36 0^{\circ} n - 9 0^{\circ}

Radians

θ = 2 \cdot 1.53000 \dots - \frac{π}{2} + 2 πn

Solution steps

\frac{1715}{70} = tan (4 5^{\circ} + \frac{θ}{2})

Switch sides

tan (4 5^{\circ} + \frac{θ}{2}) = \frac{1715}{70}

Cancel the common factor:

35

tan (4 5^{\circ} + \frac{θ}{2}) = \frac{49}{2}

Apply trig inverse properties

tan (4 5^{\circ} + \frac{θ}{2}) = \frac{49}{2}

General solutions for

tan (4 5^{\circ} + \frac{θ}{2}) = \frac{49}{2}

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

4 5^{\circ} + \frac{θ}{2} = arctan (\frac{49}{2}) + 18 0^{\circ} n

4 5^{\circ} + \frac{θ}{2} = arctan (\frac{49}{2}) + 18 0^{\circ} n

Solve

4 5^{\circ} + \frac{θ}{2} = arctan (\frac{49}{2}) + 18 0^{\circ} n : θ = 2 arctan (\frac{49}{2}) + 36 0^{\circ} n - 9 0^{\circ}

4 5^{\circ} + \frac{θ}{2} = arctan (\frac{49}{2}) + 18 0^{\circ} n

Move

4 5^{\circ}

to the right side

4 5^{\circ} + \frac{θ}{2} = arctan (\frac{49}{2}) + 18 0^{\circ} n

Subtract

4 5^{\circ}

from both sides

4 5^{\circ} + \frac{θ}{2} - 4 5^{\circ} = arctan (\frac{49}{2}) + 18 0^{\circ} n - 4 5^{\circ}

Simplify

\frac{θ}{2} = arctan (\frac{49}{2}) + 18 0^{\circ} n - 4 5^{\circ}

\frac{θ}{2} = arctan (\frac{49}{2}) + 18 0^{\circ} n - 4 5^{\circ}

Multiply both sides by

2

\frac{θ}{2} = arctan (\frac{49}{2}) + 18 0^{\circ} n - 4 5^{\circ}

Multiply both sides by

2

\frac{2 θ}{2} = 2 arctan (\frac{49}{2}) + 36 0^{\circ} n - 2 \cdot 4 5^{\circ}

Simplify

\frac{2 θ}{2} = 2 arctan (\frac{49}{2}) + 36 0^{\circ} n - 2 \cdot 4 5^{\circ}

Simplify

\frac{2 θ}{2} : θ

\frac{2 θ}{2}

Divide the numbers:

\frac{2}{2} = 1

= θ

Simplify

2 arctan (\frac{49}{2}) + 36 0^{\circ} n - 2 \cdot 4 5^{\circ} : 2 arctan (\frac{49}{2}) + 36 0^{\circ} n - 9 0^{\circ}

2 arctan (\frac{49}{2}) + 36 0^{\circ} n - 2 \cdot 4 5^{\circ}

2 \cdot 4 5^{\circ} = 9 0^{\circ}

2 \cdot 4 5^{\circ}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= 9 0^{\circ}

Cancel the common factor:

2

= 9 0^{\circ}

= 2 arctan (\frac{49}{2}) + 36 0^{\circ} n - 9 0^{\circ}

θ = 2 arctan (\frac{49}{2}) + 36 0^{\circ} n - 9 0^{\circ}

θ = 2 arctan (\frac{49}{2}) + 36 0^{\circ} n - 9 0^{\circ}

θ = 2 arctan (\frac{49}{2}) + 36 0^{\circ} n - 9 0^{\circ}

θ = 2 arctan (\frac{49}{2}) + 36 0^{\circ} n - 9 0^{\circ}

Show solutions in decimal form

θ = 2 \cdot 1.53000 \dots + 36 0^{\circ} n - 9 0^{\circ}

sin (θ) = - \frac{3}{2}, π < θ < \frac{3 π}{2}

cos (3 x) = sin (x - 3 0^{\circ})

4 sin (θ) = 4 cos (2 θ)

tan (5 θ + 30) = 1

885 cos (θ) - 70 = cos (25 0^{\circ})

What is the general solution for 1715/70 =tan(45+θ/2) ?
The general solution for 1715/70 =tan(45+θ/2) is θ=2*1.53000…+360n-90