Solve frac{2sin90^{circ}+5cos90^{circ}-3tan360^{circ}}{cos180^circsin90^circ-sin270^circsin0^circ}

$$\frac { 2 \sin 90 ^ { \circ } + 5 \cos 90 ^ { \circ } - 3 \tan 360 ^ { \circ } } { \cos 180 ^ { \circ } \sin 90 ^ { \circ } - \sin 270 ^ { \circ } \sin 0 ^ { \circ } }$$

Evaluate

$$-2$$

Solution Steps

Get the value of \sin(90) from trigonometric values table.

$$\frac{2\times 1+5\cos(90)-3\tan(360)}{\cos(180)\sin(90)-\sin(270)\sin(0)}$$

Multiply 2 and 1 to get 2.

$$\frac{2+5\cos(90)-3\tan(360)}{\cos(180)\sin(90)-\sin(270)\sin(0)}$$

Get the value of \cos(90) from trigonometric values table.

$$\frac{2+5\times 0-3\tan(360)}{\cos(180)\sin(90)-\sin(270)\sin(0)}$$

Multiply 5 and 0 to get 0.

$$\frac{2+0-3\tan(360)}{\cos(180)\sin(90)-\sin(270)\sin(0)}$$

Add 2 and 0 to get 2.

$$\frac{2-3\tan(360)}{\cos(180)\sin(90)-\sin(270)\sin(0)}$$

Get the value of \tan(360) from trigonometric values table.

$$\frac{2-3\times 0}{\cos(180)\sin(90)-\sin(270)\sin(0)}$$

Multiply 3 and 0 to get 0.

$$\frac{2-0}{\cos(180)\sin(90)-\sin(270)\sin(0)}$$

Subtract 0 from 2 to get 2.

$$\frac{2}{\cos(180)\sin(90)-\sin(270)\sin(0)}$$

Get the value of \cos(180) from trigonometric values table.

$$\frac{2}{-\sin(90)-\sin(270)\sin(0)}$$

Get the value of \sin(90) from trigonometric values table.

$$\frac{2}{-1-\sin(270)\sin(0)}$$

Get the value of \sin(270) from trigonometric values table.

$$\frac{2}{-1-\left(-\sin(0)\right)}$$

Get the value of \sin(0) from trigonometric values table.

$$\frac{2}{-1-\left(-0\right)}$$

Multiply -1 and 0 to get 0.

$$\frac{2}{-1-0}$$

Subtract 0 from -1 to get -1.

$$\frac{2}{-1}$$

Fraction \frac{2}{-1} can be rewritten as -2 by extracting the negative sign.

$$-2$$