Question

5,tan x =-, x lies in second quadrant.12

Answer 1

tanx=− 5 12

cotx= 1 tanx =− 12 5

Using Pythagorean identity,

sec 2 x− tan 2 x=1

sec 2 x− ( −5 12 ) 2 =1 sec 2 x= 25 144 +1 sec 2 x= 169 144 secx=± 13 12

Since x lies in 2nd quadrant, sec x=− 13 12 .

cos x= 1 secx = −12 13

Using Pythagorean identity,

sin 2 x+ cos 2 x=1 sinx=± 1− cos 2 x =± 1− 144 169 = 5 13 [Since x is in 2nd quadrant, sin(x) is positive]

cosec x= 1 sinx = 13 5

Hence, value of all the trigonometric functions is found.