Respuesta :
Answer:
Option A is correct.
Step-by-step explanation:
Given that
[tex]\sec{\theta}=\frac{5}{3}[/tex]
and the terminal point [tex]\theta[/tex] is in quadrant 4,
we have to check the options.
A. [tex]\cos{\theta}=\frac{3}{5}[/tex]
As in fourth quadrant [tex]\cos{\theta}[/tex] is positive.
[tex]\cos{\theta}=\frac{1}{\sec{\theta}}=\frac{1}{\frac{5}{3}}=\frac{3}{5}[/tex]
which is correct option.
As in fourth quadrant all trigonometric functions are negative except [tex]\cos{\theta} \thinspace and\thinspace \sec{\theta}[/tex]
gives second and third option are not correct.
[tex]sin{\theta}=\pm\sqrt{1-\cos^2{\theta}}=\pm\sqrt{1-(\frac{3}{5})^2)}=\pm\sqrt{1-\frac{9}{25}}=\pm\sqrt{\frac{16}{25}}=-\frac{4}{5}[/tex]
Hence, only first option is correct.
Answer:
option A) and B) are the CORRECT answers
Step-by-step explanation:
