What is the value of sin(5)cos(25)+cos(5)sin(25) ?

The value of sin(5)cos(25)+cos(5)sin(25) is 1/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sin(5)cos(25)+cos(5)sin(25)

sin (5^{\circ}) cos (2 5^{\circ}) + cos (5^{\circ}) sin (2 5^{\circ})

\frac{1}{2}

Decimal Notation

0.5

Solution steps

sin (5^{\circ}) cos (2 5^{\circ}) + cos (5^{\circ}) sin (2 5^{\circ})

Rewrite using trig identities:

sin (3 0^{\circ})

sin (5^{\circ}) cos (2 5^{\circ}) + cos (5^{\circ}) sin (2 5^{\circ})

Use the Angle Sum identity:

sin (s) cos (t) + cos (s) sin (t) = sin (s + t)

= sin (5^{\circ} + 2 5^{\circ})

Simplify

= sin (3 0^{\circ})

= sin (3 0^{\circ})

Use the following trivial identity:

sin (3 0^{\circ}) = \frac{1}{2}

sin (3 0^{\circ})

sin (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{1}{2}

= \frac{1}{2}

- \frac{2}{3} cot (\frac{π}{4})

sin (\frac{8}{3} π)

0.06 e^{- 43.1 \cdot 0.2} sin (90.2352 \cdot 0.2)

tan (\frac{7 π}{12}) + cot (\frac{5 π}{12})

sin (arccos (- 1) - arccos (\frac{1}{2}))

What is the value of sin(5)cos(25)+cos(5)sin(25) ?
The value of sin(5)cos(25)+cos(5)sin(25) is 1/2