Question

if x =13/5and x lies in 2nd quadrantfind values of other 5 trignometrical funcrions​

Answer 1

1) sec X = 13/5

x lies in 4th quadrant.

cos X = 1/ secx

\cos(x) = \frac{1}{ \frac{13}{5} } = \frac{5}{13}cos(x)=5131=135

2) So, cos x = 5/13

sin X = √ 1- cos²x

\sin(x) = \sqrt{1 - ( { \frac{5}{13} )}^{2} }sin(x)=1−(135)2

3) sin X = -12/13

⚆As sin functions-ve in 4th quadrant.

cosec X = 1/sin X

\csc(x) = \frac{1}{ \frac{ - 12}{13} }csc(x)=13−121

4) cosec X = -13/12

⚆As cosec functions-ve in 4th quadrant.

tan X = √ sec² x-1

\tan(x) = \sqrt{ { \frac{13}{5} }^{2} - 1 }tan(x)=5132−1

5)tan X = -12/5

⚆As tan functions-ve in 4th quadrant.

Cot x = 1/ tan X

\cot(x) = \frac{1}{ \frac{ - 12}{5} }cot(x)=5−121

\cot(x) = - \frac{5}{12}cot(x)=−125

6)Cot x = -5/12