Question

8-2: practice & problem-solving day 1
part 1 of 6
write the ratios for sin m, cos m, and tan m. give the exact value and a four-decimal approximation.
sin m=□
(type an exact answer in simplified form. type an integer or a fraction.)
due
feb 12-12.00 am

Explanation:

Step1: Recall sine definition

For angle $M$ in right $\triangle MKL$, $\sin M = \frac{\text{opposite side}}{\text{hypotenuse}}$

Step2: Identify sides for $\sin M$

Opposite side to $M$ is $KL = 4\sqrt{3}$, hypotenuse $ML = 8$
<Expression>
$\sin M = \frac{4\sqrt{3}}{8}$
</Expression>

Step3: Simplify the fraction

Cancel common factor 4 in numerator and denominator
<Expression>
$\sin M = \frac{\sqrt{3}}{2}$
</Expression>

Step4: Calculate decimal approximation

Compute the decimal value of $\frac{\sqrt{3}}{2}$
<Expression>
$\frac{\sqrt{3}}{2} \approx 0.8660$
</Expression>

Answer:

Exact value: $\frac{\sqrt{3}}{2}$
Four-decimal approximation: $0.8660$