What is the value of 2+sin(pi/4)-3tan(pi/4) ?

The value of 2+sin(pi/4)-3tan(pi/4) is (sqrt(2))/2-1

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

2+sin(pi/4)-3tan(pi/4)

2 + sin (\frac{π}{4}) - 3 tan (\frac{π}{4})

\frac{2}{2} - 1

Decimal Notation

- 0.29289 \dots

Solution steps

2 + sin (\frac{π}{4}) - 3 tan (\frac{π}{4})

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:

tan (\frac{π}{4}) = 1

tan (\frac{π}{4})

tan (x)

periodicity table with

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} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

= 1

= 2 + \frac{2}{2} - 3 \cdot 1

Simplify

= \frac{2}{2} - 1

arcsin (sin (\frac{11 π}{9}))

15 sin (5 0^{\circ})

sin (4 \frac{π}{2})

arccos (\frac{2}{9})

\frac{22}{sin ( 5 4 ^{\circ} )}

What is the value of 2+sin(pi/4)-3tan(pi/4) ?
The value of 2+sin(pi/4)-3tan(pi/4) is (sqrt(2))/2-1