What is the general solution for 189.4=100tan^2(45+θ/2) ?

The general solution for 189.4=100tan^2(45+θ/2) is θ=2*0.94242…+360n-90,θ=-2*0.94242…+360n-90

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189.4=100tan^2(45+θ/2)

189.4 = 100 tan^{2} (4 5^{\circ} + \frac{θ}{2})

θ = 2 \cdot 0.94242 \dots + 36 0^{\circ} n - 9 0^{\circ}, θ = - 2 \cdot 0.94242 \dots + 36 0^{\circ} n - 9 0^{\circ}

Solution steps

189.4 = 100 tan^{2} (4 5^{\circ} + \frac{θ}{2})

Switch sides

100 tan^{2} (4 5^{\circ} + \frac{θ}{2}) = 189.4

Solve by substitution

tan (4 5^{\circ} + \frac{θ}{2}) = 1.894, tan (4 5^{\circ} + \frac{θ}{2}) = - 1.894

tan (4 5^{\circ} + \frac{θ}{2}) = 1.894 : θ = 2 arctan (1.894) + 36 0^{\circ} n - 9 0^{\circ}

tan (4 5^{\circ} + \frac{θ}{2}) = - 1.894 : θ = - 2 arctan (1.894) + 36 0^{\circ} n - 9 0^{\circ}

Combine all the solutions

θ = 2 arctan (1.894) + 36 0^{\circ} n - 9 0^{\circ}, θ = - 2 arctan (1.894) + 36 0^{\circ} n - 9 0^{\circ}

Show solutions in decimal form

θ = 2 \cdot 0.94242 \dots + 36 0^{\circ} n - 9 0^{\circ}, θ = - 2 \cdot 0.94242 \dots + 36 0^{\circ} n - 9 0^{\circ}

csc (θ) = 1 + cot (θ)

cos (2 x) = 0.98

8 sin^{2} (x) + 2 sin (x) - 3 = 0

2 (arcsin (x))^{2} + (2 - π) arcsin (x) - π = 0

cos^{2} (x) + 3 sin (- x) - 2 = 0

What is the general solution for 189.4=100tan^2(45+θ/2) ?
The general solution for 189.4=100tan^2(45+θ/2) is θ=2*0.94242…+360n-90,θ=-2*0.94242…+360n-90