What is the value of sin(60)cos(60)tan(60)cot(60)sec(60)csc(60) ?

The value of sin(60)cos(60)tan(60)cot(60)sec(60)csc(60) is 1

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sin(60)cos(60)tan(60)cot(60)sec(60)csc(60)

Solution

sin (6 0^{\circ}) cos (6 0^{\circ}) tan (6 0^{\circ}) cot (6 0^{\circ}) sec (6 0^{\circ}) csc (6 0^{\circ})

Solution

1

Solution steps

sin (6 0^{\circ}) cos (6 0^{\circ}) tan (6 0^{\circ}) cot (6 0^{\circ}) sec (6 0^{\circ}) csc (6 0^{\circ})

Use the following trivial identity:

sin (6 0^{\circ}) = \frac{3}{2}

sin (6 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{3}{2}

Use the following trivial identity:

cos (6 0^{\circ}) = \frac{1}{2}

cos (6 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{1}{2}

Use the following trivial identity:

tan (6 0^{\circ}) = 3

tan (6 0^{\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}

= 3

Use the following trivial identity:

cot (6 0^{\circ}) = \frac{3}{3}

cot (6 0^{\circ})

cot (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} cot (x) \mp \infty 31 \frac{3}{3} 0 - \frac{3}{3} - 1 - 3

= \frac{3}{3}

Use the following trivial identity:

sec (6 0^{\circ}) = 2

sec (6 0^{\circ})

sec (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} sec (x) 1 \frac{2 3}{3} 22 Undefined - 2 - 2 - \frac{2 3}{3} 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} sec (x) - 1 - \frac{2 3}{3} - 2 - 2 Undefined 22 \frac{2 3}{3}

= 2

Use the following trivial identity:

csc (6 0^{\circ}) = \frac{2 3}{3}

csc (6 0^{\circ})

csc (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} csc (x) Undefiend 22 \frac{2 3}{3} 1 \frac{2 3}{3} 22 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} csc (x) Undefiend - 2 - 2 - \frac{2 3}{3} - 1 - \frac{2 3}{3} - 2 - 2

= \frac{2 3}{3}

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

Simplify

\frac{3}{2} \cdot \frac{1}{2} 3 \frac{3}{3} \cdot 2 \cdot \frac{2 3}{3} : 1

\frac{3}{2} \cdot \frac{1}{2} 3 \frac{3}{3} \cdot 2 \cdot \frac{2 3}{3}

Multiply fractions:

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

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

Cancel the common factor:

2

= \frac{3 \cdot 1 \cdot 3 3 3}{3 \cdot 3}

3 \cdot 1 \cdot 333 = 3^{4 \cdot \frac{1}{2}}

3 \cdot 1 \cdot 333

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

3333 = 3^{\frac{1}{2}} \cdot 3^{\frac{1}{2}} \cdot 3^{\frac{1}{2}} \cdot 3^{\frac{1}{2}} = 3^{\frac{1}{2} + \frac{1}{2} + \frac{1}{2} + \frac{1}{2}}

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

Add similar elements:

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

= 1 \cdot 3^{4 \cdot \frac{1}{2}}

Multiply:

1 \cdot 3^{4 \cdot \frac{1}{2}} = 3^{4 \cdot \frac{1}{2}}

= 3^{4 \cdot \frac{1}{2}}

= \frac{3 ^{4 \cdot \frac{1}{2}}}{3 \cdot 3}

Multiply the numbers:

3 \cdot 3 = 9

= \frac{3 ^{4 \cdot \frac{1}{2}}}{9}

Factor

9 : 3^{2}

Factor

9 = 3^{2}

= \frac{3 ^{4 \cdot \frac{1}{2}}}{3 ^{2}}

Cancel the common factor:

3^{4 \cdot \frac{1}{2}}

= 1

= 1

Popular Examples

arcsin((sin(35.5))/(1.333))

arcsin (\frac{sin ( 35. 5 ^{\circ} )}{1.333})

10sin(pi/6 5)

10 sin (\frac{π}{6} 5)

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

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

sin(5/6)pi

sin (\frac{5}{6}) π

arcsin(cos(30))

arcsin (cos (3 0^{\circ}))

Frequently Asked Questions (FAQ)

What is the value of sin(60)cos(60)tan(60)cot(60)sec(60)csc(60) ?
The value of sin(60)cos(60)tan(60)cot(60)sec(60)csc(60) is 1