3 years ago

Find the value of x in each case.

Mathematics

1 answer:

ExtremeBDS [4]3 years ago

5 0

62 is the awnser for this

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URGENT: If θ is a second-quadrant angle and cosθ = -2/3, then tanθ = _____.

dangina [55]

In the second quadrant, both cos and tan are negative while only sin is positive.

To find tan, we will use the following property below:

$\large \boxed{ {tan}^{2} \theta = {sec}^{2} \theta - 1}$

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$\large{ {tan}^{2} \theta = {( - \frac{3}{2}) }^{2} - 1} \\ \large{ {tan}^{2} \theta = \frac{9}{4} - 1} \\ \large{ {tan}^{2} \theta = \frac{9}{4} - \frac{4}{4} \longrightarrow \frac{5}{4} } \\ \large{tan \theta = \frac{ \sqrt{5} }{ \sqrt{4} } } \\ \large \boxed{tan \theta = \frac{ \sqrt{5} }{2} }$

Since tan is negative in the second quadrant. Hence,

$\large{ \cancel{ tan \theta = \frac{ \sqrt{5} }{2} } \longrightarrow \boxed{tan \theta = - \frac{ \sqrt{5} }{2} }}$

Answer

tan = -√5/2

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2 years ago