Question

If cos x = 3/5 and x is in 4th Quadrant,then tan x is ?

Answer 1

x in 4th quadrant

cosx= 3/5

=> sinx = - 4/5

tanx = sinx/cosx = (-4/5)/(3/5)

=> tanx = - 4/3

Answer 2

The value of tanx = - 4/3

Given :

cosx = 3/5 and x is in 4th Quadrant

To find :

The value of tanx

Solution :

Step 1 of 2 :

Find the sign of tanx

cosx = 3/5

x is in 4th Quadrant

∴ tanx is negative

Step 2 of 2 :

Find the value of tanx

$\displaystyle \sf cosx = \frac{3}{5}$

$\displaystyle \sf{ \implies }secx = \frac{5}{3}$

$\displaystyle \sf{ \implies } {sec}^{2}x - 1 = \frac{25}{9} - 1$

$\displaystyle \sf{ \implies } {tan}^{2}x = \frac{25 - 9}{9}$

$\displaystyle \sf{ \implies } {tan}^{2}x = \frac{16}{9}$

$\displaystyle \sf{ \implies } {tan}^{}x = \pm \frac{4}{3}$

Since tanx is negative

$\displaystyle \sf{ \therefore \: \: } {tan}^{}x = - \frac{4}{3}$

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