Question

question 15
use a graphing calculator to evaluate. round to 3 decimal places.
\\( \sin \left( \frac { 5 } { 12 } \pi \
ight) = \\)
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Explanation:

Step1: Convert the angle to degrees

We know that \(\pi\) radians \( = 180^{\circ}\). So, \(\frac{5}{12}\pi=\frac{5}{12}\times180^{\circ}=75^{\circ}\)

Step2: Use the calculator

On a graphing calculator, make sure it is in degree mode. Then enter \(\sin(75^{\circ})\)
\(\sin(75^{\circ})=\sin(45^{\circ} + 30^{\circ})\)
Using the formula \(\sin(A + B)=\sin A\cos B+\cos A\sin B\) where \(A = 45^{\circ}\), \(B=30^{\circ}\)
\(\sin(45^{\circ})\cos(30^{\circ})+\cos(45^{\circ})\sin(30^{\circ})=\frac{\sqrt{2}}{2}\times\frac{\sqrt{3}}{2}+\frac{\sqrt{2}}{2}\times\frac{1}{2}=\frac{\sqrt{6}+\sqrt{2}}{4}\approx0.966\)

Answer:

\(0.966\)