Solve 3sin(60)cos(45-15)

$$3 \sin ( 60 ) \cos ( 45-15 )$$

Evaluate

$$\frac{9}{4}=2.25$$

Solution Steps

Get the value of \sin(60) from trigonometric values table.

$$3\times \frac{\sqrt{3}}{2}\cos(45-15)$$

Subtract 15 from 45 to get 30.

$$3\times \frac{\sqrt{3}}{2}\cos(30)$$

Get the value of \cos(30) from trigonometric values table.

$$3\times \frac{\sqrt{3}}{2}\times \frac{\sqrt{3}}{2}$$

Multiply \frac{\sqrt{3}}{2} and \frac{\sqrt{3}}{2} to get \left(\frac{\sqrt{3}}{2}\right)^{2}.

$$3\times \left(\frac{\sqrt{3}}{2}\right)^{2}$$

To raise \frac{\sqrt{3}}{2} to a power, raise both numerator and denominator to the power and then divide.

$$3\times \frac{\left(\sqrt{3}\right)^{2}}{2^{2}}$$

Express 3\times \frac{\left(\sqrt{3}\right)^{2}}{2^{2}} as a single fraction.

$$\frac{3\left(\sqrt{3}\right)^{2}}{2^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{3\times 3}{2^{2}}$$

Multiply 3 and 3 to get 9.

$$\frac{9}{2^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{9}{4}$$