Math  /  Trigonometry

QuestionSolve the equation 8tan(4θ)+3=118 \tan (4 \theta)+3=11 for a value of θ\theta in the first quadrant. Give your answer in radians and degrees. θ=\theta= \square radians, to 4 decimal places or \square degrees.

Studdy Solution
Convert θ\theta from radians to degrees. We know that 180=π180^\circ = \pi radians, so:
θ=π16×180π \theta = \frac{\pi}{16} \times \frac{180^\circ}{\pi} θ=18016 \theta = \frac{180^\circ}{16} θ=11.25 \theta = 11.25^\circ
The value of θ\theta is:
θ=π16 radians, or 11.25 \theta = \frac{\pi}{16} \text{ radians, or } 11.25^\circ

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