chelseacharupickard
Answered

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

Sagot :

sreedevi102

Answer:

[tex]14 tan\theta = -48[/tex]

Step-by-step explanation:

[tex]cos \theta = \frac{-7}{25}\\\\cos^2 \theta = \frac{49}{625}\\\\sin^2 \theta = 1 - cos^2 \theta\\\\[/tex]

        [tex]=1 - \frac{49}{625}\\\\=\frac{625-49}{625}\\\\=\frac{576}{625}\\\\[/tex]

[tex]sin \theta = \sqrt{\frac{576}{625}} = \frac{24}{25}[/tex]

[tex]tan \theta = \frac{sin \theta}{cos \theta}[/tex]

          [tex]=\frac{\frac{24}{25}}{\frac{-7}{25}}\\\\=\frac{24}{25} \times \frac{25}{-7}\\\\=\frac{-24}{7}[/tex]

[tex]14 tan \theta = 14 \times \frac{-24}{7} = 2 \times -24 = -48[/tex]

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