What is the value of (tan(225))/(sin(330)) ?

The value of (tan(225))/(sin(330)) is -2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(tan(225))/(sin(330))

Solution

\frac{tan ( 22 5 ^{\circ} )}{sin ( 33 0 ^{\circ} )}

Solution

- 2

Solution steps

\frac{tan ( 22 5 ^{\circ} )}{sin ( 33 0 ^{\circ} )}

Rewrite using trig identities:

tan (22 5^{\circ}) = 1

tan (22 5^{\circ})

tan (22 5^{\circ}) = tan (4 5^{\circ})

tan (22 5^{\circ})

Rewrite

22 5^{\circ}

18 0^{\circ} + 4 5^{\circ}

= tan (18 0^{\circ} + 4 5^{\circ})

Apply the periodicity of

tan

tan (x + 18 0^{\circ}) = tan (x)

tan (18 0^{\circ} + 4 5^{\circ}) = tan (4 5^{\circ})

= tan (4 5^{\circ})

= tan (4 5^{\circ})

Use the following trivial identity:

tan (4 5^{\circ}) = 1

tan (4 5^{\circ})

tan (x)

periodicity table with

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

= 1

= 1

Rewrite using trig identities:

sin (33 0^{\circ}) = - \frac{1}{2}

sin (33 0^{\circ})

Rewrite using trig identities:

sin (18 0^{\circ}) cos (15 0^{\circ}) + cos (18 0^{\circ}) sin (15 0^{\circ})

sin (33 0^{\circ})

Write

sin (33 0^{\circ})

sin (18 0^{\circ} + 15 0^{\circ})

= sin (18 0^{\circ} + 15 0^{\circ})

Use the Angle Sum identity:

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

= sin (18 0^{\circ}) cos (15 0^{\circ}) + cos (18 0^{\circ}) sin (15 0^{\circ})

= sin (18 0^{\circ}) cos (15 0^{\circ}) + cos (18 0^{\circ}) sin (15 0^{\circ})

Use the following trivial identity:

sin (18 0^{\circ}) = 0

sin (18 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}

= 0

Use the following trivial identity:

cos (15 0^{\circ}) = - \frac{3}{2}

cos (15 0^{\circ})

cos (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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{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} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= - \frac{3}{2}

Use the following trivial identity:

cos (18 0^{\circ}) = (- 1)

cos (18 0^{\circ})

cos (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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{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} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= (- 1)

Use the following trivial identity:

sin (15 0^{\circ}) = \frac{1}{2}

sin (15 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}

= 0 \cdot (- \frac{3}{2}) + (- 1) \frac{1}{2}

Simplify

= - \frac{1}{2}

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

Simplify

= - 2

Popular Examples

cos(-1410)

cos (- 141 0^{\circ})

4+3cos(pi/3)

4 + 3 cos (\frac{π}{3})

arctan(-0.09)

arctan (- 0.09)

arccos(1/2)+2arcsin(1/2)

arccos (\frac{1}{2}) + 2 arcsin (\frac{1}{2})

(tan(300))/(sin(120))

\frac{tan ( 30 0 ^{\circ} )}{sin ( 12 0 ^{\circ} )}

Frequently Asked Questions (FAQ)

What is the value of (tan(225))/(sin(330)) ?
The value of (tan(225))/(sin(330)) is -2