Question

Given that tanx=14 and sinx is negative, determine sin(2x), cos(2x), and tan(2x). Write the exact answer. Do not round.

Answer 1

By applying trigonometric identities, the value of tan(x) = 14, gives;

$sin(2 \cdot x) = \frac{28}{197}$

$cos(2 \cdot x) = -\frac{195}{197}$

$tan(2 \cdot x) = -\frac{28}{195}$

Which method can be used to find the value of the trigonometric expressions?

Given;

tan(x) = 14

sin(x) is negative

By definition, we have;

$sin(2 \cdot x) = \mathbf{\frac{2 \cdot \: tan(x)}{1 + {tan(x)}^{2} }}$

Which gives;

$sin(2 \cdot x) = \frac{2 \times 14}{1 + {14}^{2} } = \frac{28}{197}$

Similarly, we have;

$cos(2 \cdot x) = \mathbf{\frac{1- tan(x)^2}{1 + {tan(x)}^{2} }}$

Which gives;

$cos(2 \cdot x) = \frac{1- 14^2}{1 + {14}^{2} } = -\frac{195}{197}$

$tan(2 \cdot x) = \mathbf{\frac{sin(2 \cdot x) }{cos(2 \cdot x) } }$

Which gives;

$tan(2 \cdot x) = \frac{ \frac{28}{197}}{-\frac{195}{197} } = -\frac{28}{195}$

Learn more about trigonometric identities and functions here:

https://brainly.com/question/7331447

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