Question

which equation is true? \\(\sin(x) = 6/8\\) \\(\cos(x) = 6/6\\) \\(\cos(x) = 6/8\\) \\(\tan(x) = 6/8\\)

Explanation:

Step1: Identify trigonometric ratios

For an acute angle $x$ in a right triangle:

• $\sin(x)=\frac{\text{opposite}}{\text{hypotenuse}}$, $\cos(x)=\frac{\text{adjacent}}{\text{hypotenuse}}$, $\tan(x)=\frac{\text{opposite}}{\text{adjacent}}$

Step2: Match sides to angle $x$

Opposite side to $x$: $6$, adjacent side to $x$: $8$, hypotenuse: $\sqrt{6^2+8^2}=10$ (not needed for options)

Step3: Evaluate each option

• $\sin(x)=\frac{6}{10}

eq\frac{6}{8}$

• $\cos(x)=\frac{8}{10}

eq\frac{8}{6}$

• $\cos(x)=\frac{8}{10}

eq\frac{6}{8}$

• $\tan(x)=\frac{6}{8}$ (matches, since $\tan(x)=\frac{\text{opposite}}{\text{adjacent}}=\frac{6}{8}$)

Answer:

tan (x) = 6/8