Solve 2sin(45)+3cos(45)

$$2 \sin ( 45 ) +3 \cos ( 45 )$$

Evaluate

$$\frac{5\sqrt{2}}{2}\approx 3.535533906$$

Solution Steps

Get the value of \sin(45) from trigonometric values table.

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

Cancel out 2 and 2.

$$\sqrt{2}+3\cos(45)$$

Get the value of \cos(45) from trigonometric values table.

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

Express 3\times \frac{\sqrt{2}}{2} as a single fraction.

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

Combine \sqrt{2} and \frac{3\sqrt{2}}{2} to get \frac{5}{2}\sqrt{2}.

$$\frac{5}{2}\sqrt{2}$$