What is the value of -1/2 sin(pi/2)-4cos(pi) ?

The value of -1/2 sin(pi/2)-4cos(pi) is 7/2

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-1/2 sin(pi/2)-4cos(pi)

- \frac{1}{2} sin (\frac{π}{2}) - 4 cos (π)

\frac{7}{2}

Decimal Notation

3.5

Solution steps

- \frac{1}{2} sin (\frac{π}{2}) - 4 cos (π)

Use the following trivial identity:

sin (\frac{π}{2}) = 1

sin (\frac{π}{2})

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= 1

Use the following trivial identity:

cos (π) = (- 1)

cos (π)

cos (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= (- 1)

= - \frac{1}{2} \cdot 1 - 4 (- 1)

Simplify

- \frac{1}{2} \cdot 1 - 4 (- 1) : \frac{7}{2}

- \frac{1}{2} \cdot 1 - 4 (- 1)

Apply rule

- (- a) = a

= - \frac{1}{2} \cdot 1 + 4 \cdot 1

Multiply:

\frac{1}{2} \cdot 1 = \frac{1}{2}

= - \frac{1}{2} + 4 \cdot 1

Multiply the numbers:

4 \cdot 1 = 4

= - \frac{1}{2} + 4

Convert element to fraction:

4 = \frac{4 \cdot 2}{2}

= \frac{4 \cdot 2}{2} - \frac{1}{2}

Since the denominators are equal, combine the fractions:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{4 \cdot 2 - 1}{2}

4 \cdot 2 - 1 = 7

4 \cdot 2 - 1

Multiply the numbers:

4 \cdot 2 = 8

= 8 - 1

Subtract the numbers:

8 - 1 = 7

= 7

= \frac{7}{2}

= \frac{7}{2}

tan (\frac{5 π}{2}) - 2 π

\frac{1}{cos ^{2} ( \frac{3 π}{4} )}

sin (\frac{1}{2})

sec^{2} (2 \cdot \frac{π}{6})

tan (6 0^{\circ}) + 2 tan (3 0^{\circ})

What is the value of -1/2 sin(pi/2)-4cos(pi) ?
The value of -1/2 sin(pi/2)-4cos(pi) is 7/2