Question

If $\cos \theta =\frac{7}{25}$ and $\theta$ is in fourth quadrant, then remaining trigonometric ratios are

• A. $\sin \theta =-\frac{24}{25}$
• B. $\tan \theta =-\frac{24}{7}$
• C. $\csc \theta =-\frac{25}{24}$
• D. $\cot \theta =-\frac{7}{24}$

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A $\sin \theta =-\frac{24}{25}$
B $\tan \theta =-\frac{24}{7}$
C $\csc \theta =-\frac{25}{24}$
D $\cot \theta =-\frac{7}{24}$

$cos\theta =\frac{7}{25}$

$cos\theta =\frac{B}{H}=\frac{7}{25}$

$B=7$, $H=25$

Thus, by Pythagoras Theorem,

$H^2=B^2+P^2$

${25}^2=7^2+P^2$

$P^2=576$

$P=24$ cm

Since, $\theta$ is in fourth quadrant, all values will be negative except, $\cos \theta$ and $sec\theta$

$\sin \theta =\frac{P}{H}=-\frac{24}{25}$

$\tan \theta =\frac{P}{B}=-\frac{24}{7}$

$\csc \theta =\frac{H}{P}=-\frac{25}{24}$

$\sec \theta =\frac{H}{B}=\frac{25}{7}$

$\cot \theta =\frac{B}{P}=-\frac{7}{24}$