Question

If cos theta is equal to -7/25 and theta (180°;360°) what is the value of 14 tan theta ​

Answer 1

Answer:

$14 tan\theta = -48$

Step-by-step explanation:

$cos \theta = \frac{-7}{25}\\\\cos^2 \theta = \frac{49}{625}\\\\sin^2 \theta = 1 - cos^2 \theta$

        $=1 - \frac{49}{625}\\\\=\frac{625-49}{625}\\\\=\frac{576}{625}$

$sin \theta = \sqrt{\frac{576}{625}} = \frac{24}{25}$

$tan \theta = \frac{sin \theta}{cos \theta}$

          $=\frac{\frac{24}{25}}{\frac{-7}{25}}\\\\=\frac{24}{25} \times \frac{25}{-7}\\\\=\frac{-24}{7}$

$14 tan \theta = 14 \times \frac{-24}{7} = 2 \times -24 = -48$