Solve sin(pi/6left(tan(pi/4)+cos(pi/3)right))

$$\sin ( \frac{ \pi }{ 6 } \left( \tan ( \frac{ \pi }{ 4 } ) + \cos ( \frac{ \pi }{ 3 } ) \right) )$$

Evaluate

$$\frac{\sqrt{2}}{2}\approx 0.707106781$$

Solution Steps

Get the value of \tan(\frac{\pi }{4}) from trigonometric values table.

$$\sin(\frac{\pi }{6}\left(1+\cos(\frac{\pi }{3})\right))$$

Get the value of \cos(\frac{\pi }{3}) from trigonometric values table.

$$\sin(\frac{\pi }{6}\left(1+\frac{1}{2}\right))$$

Add 1 and \frac{1}{2} to get \frac{3}{2}.

$$\sin(\frac{\pi }{6}\times \frac{3}{2})$$

Multiply \frac{\pi }{6} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\sin(\frac{\pi \times 3}{6\times 2})$$

Cancel out 3 in both numerator and denominator.

$$\sin(\frac{\pi }{2\times 2})$$

Multiply 2 and 2 to get 4.

$$\sin(\frac{\pi }{4})$$

Get the value of \sin(\frac{\pi }{4}) from trigonometric values table.

$$\frac{\sqrt{2}}{2}$$