Question

question 29 (1 point)
the point (3,4) is on the terminal arm of ∠a. which is the set of exact primary trigonometric ratios for the angle?
a) sin a = 3/5, cos a = 4/5, tan a = 3/4
b) sin a = 5/4, cos a = 5/3, tan a = 3/4
c) sin a = 4/5, cos a = 3/5, tan a = 4/3
d) sin a = 4/5, cos a = 3/5, tan a = 4/3

Explanation:

Step1: Calculate the hypotenuse \( r \)

For a point \((x,y)=(3,4)\) on the terminal arm of an angle, use the formula \( r=\sqrt{x^{2}+y^{2}} \).
\( r = \sqrt{3^{2}+4^{2}}=\sqrt{9 + 16}=\sqrt{25}=5 \)

Step2: Calculate \(\sin A\), \(\cos A\), and \(\tan A\)

The definitions of trigonometric ratios are:

• \(\sin A=\frac{y}{r}\), so \(\sin A=\frac{4}{5}\)
• \(\cos A=\frac{x}{r}\), so \(\cos A=\frac{3}{5}\)
• \(\tan A=\frac{y}{x}\), so \(\tan A=\frac{4}{3}\)

Answer:

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