What is the value of sin(pi/4)-4cos(pi/3) ?

The value of sin(pi/4)-4cos(pi/3) is (sqrt(2))/2-2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sin(pi/4)-4cos(pi/3)

sin (\frac{π}{4}) - 4 cos (\frac{π}{3})

\frac{2}{2} - 2

Decimal Notation

- 1.29289 \dots

Solution steps

sin (\frac{π}{4}) - 4 cos (\frac{π}{3})

Use the following trivial identity:

sin (\frac{π}{4}) = \frac{2}{2}

sin (\frac{π}{4})

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}

= \frac{2}{2}

Use the following trivial identity:

cos (\frac{π}{3}) = \frac{1}{2}

cos (\frac{π}{3})

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}

= \frac{1}{2}

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

Simplify

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

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

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

4 \cdot \frac{1}{2}

Multiply fractions:

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

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

Multiply the numbers:

1 \cdot 4 = 4

= \frac{4}{2}

Divide the numbers:

\frac{4}{2} = 2

= 2

= \frac{2}{2} - 2

= \frac{2}{2} - 2

tan (- 66 0^{\circ})

30 \cdot csc (4 5^{\circ})

sin (2 \frac{1}{3})

cos (7 0^{\circ}) 10

3.5 \cdot cos (3.5 \cdot 2.4 - 0.8)

What is the value of sin(pi/4)-4cos(pi/3) ?
The value of sin(pi/4)-4cos(pi/3) is (sqrt(2))/2-2