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