Question

Find the values of other five trigonometric functions if $sin\,x=-\frac{3}{5},$ x lies in second quadrant.

Answer 1

$sin\,x=\frac{3}{2}$

$cosec\,x=\frac{1}{sin\,x}=\frac{1}{(\frac{3}{5})}=\frac{5}{3}$

$sin^2x+cos^2\,x=1$

$⇒cos^2x=1-sin^2x$

$⇒cos^2x=1-(\frac{3}{5})^2$

$⇒cos^2x=1-\frac{9}{25}$

$⇒cos^2\,x=\frac{16}{25}$

$⇒cos^2\,x=±\frac{4}{5}$

Since x lies in the 2nd quadrant, the value of cos x will be negative

$∴cos\,x=-\frac{4}{5}$

$sec\,x=\frac{1}{cos\,\,x}=\frac{1}{(-\frac{4}{5})}=-\frac{5}{4}$

$tan\,x=\frac{sin\,x}{cos \,x}=\frac{(\frac{3}{5})}{(-\frac{4}{5})}=\frac{3}{4}$

$cot\,x=\frac{1}{tan\,x}=\frac{4}{3}$