Question

question 21 (1 point)
the point (3, 4) is on the terminal arm of da. which is the set of exact primary trigonometric ratios for the angle?
o a) sin a = 4/5, cos a = 3/5, tan a = 3/4
o b) sin a = 5/4, cos a = 5/3, tan a = 3/4
o c) sin a = 3/5, cos a = 4/5, tan a = 4/3
o d) sin a = 4/5, cos a = 3/5, tan a = 4/3

Explanation:

Step1: Calculate the hypotenuse \( r \)

Using the Pythagorean theorem \( r=\sqrt{x^{2}+y^{2}} \), where \( x = 3 \) and \( y = 4 \).
\( r=\sqrt{3^{2}+4^{2}}=\sqrt{9 + 16}=\sqrt{25}=5 \)

Step2: Calculate \( \sin A \)

\( \sin A=\frac{y}{r} \), substituting \( y = 4 \) and \( r = 5 \)
\( \sin A=\frac{4}{5} \)

Step3: Calculate \( \cos A \)

\( \cos A=\frac{x}{r} \), substituting \( x = 3 \) and \( r = 5 \)
\( \cos A=\frac{3}{5} \)

Step4: Calculate \( \tan A \)

\( \tan A=\frac{y}{x} \), substituting \( y = 4 \) and \( x = 3 \)
\( \tan A=\frac{4}{3} \)

Answer:

D. \( \sin A=\frac{4}{5},\cos A=\frac{3}{5},\tan A=\frac{4}{3} \)