Questions: Find the exact value of the sine and cosine of angle θ when θ=π/3 This problem should be done without the assistance of a calculator. To Enter something like √2, type sqrt to get the √ symbol and then type 2 or click in the answer box to get the tool palette. Use the right arrow to get out from under the radical sign. sin (θ)= cos (θ)=

Solution Steps

To find the exact values of the sine and cosine of the angle \(\theta = \frac{\pi}{3}\), we can use the known values from the unit circle. The angle \(\frac{\pi}{3}\) radians corresponds to 60 degrees. On the unit circle, the sine of 60 degrees is \(\frac{\sqrt{3}}{2}\) and the cosine of 60 degrees is \(\frac{1}{2}\).

The angle given is \(\theta = \frac{\pi}{3}\), which corresponds to 60 degrees.

For \(\theta = \frac{\pi}{3}\), the known values from the unit circle are:

• \(\sin\left(\frac{\pi}{3}\right) = \frac{\sqrt{3}}{2}\)
• \(\cos\left(\frac{\pi}{3}\right) = \frac{1}{2}\)

The calculated values are:

• \(\sin\left(\frac{\pi}{3}\right) \approx 0.8660\)
• \(\cos\left(\frac{\pi}{3}\right) \approx 0.5000\)

These approximate values match the known exact values:

• \(\sin\left(\frac{\pi}{3}\right) = \frac{\sqrt{3}}{2} \approx 0.8660\)
• \(\cos\left(\frac{\pi}{3}\right) = \frac{1}{2} \approx 0.5000\)

Final Answer