What is the value of sin^2(30)+sec^2(45)-6cos(60) ?

The value of sin^2(30)+sec^2(45)-6cos(60) is -3/4

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sin^2(30)+sec^2(45)-6cos(60)

Solution

sin^{2} (3 0^{\circ}) + sec^{2} (4 5^{\circ}) - 6 cos (6 0^{\circ})

Solution

- \frac{3}{4}

Decimal Notation

- 0.75

Solution steps

sin^{2} (3 0^{\circ}) + sec^{2} (4 5^{\circ}) - 6 cos (6 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}

Use the following trivial identity:

sec (4 5^{\circ}) = 2

sec (4 5^{\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:

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}

= (\frac{1}{2})^{2} + (2)^{2} - 6 \cdot \frac{1}{2}

Simplify

(\frac{1}{2})^{2} + (2)^{2} - 6 \cdot \frac{1}{2} : - \frac{3}{4}

(\frac{1}{2})^{2} + (2)^{2} - 6 \cdot \frac{1}{2}

(\frac{1}{2})^{2} = \frac{1}{2 ^{2}}

(\frac{1}{2})^{2}

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{1 ^{2}}{2 ^{2}}

Apply rule

1^{a} = 1

1^{2} = 1

= \frac{1}{2 ^{2}}

(2)^{2} = 2

(2)^{2}

Apply radical rule:

a = a^{\frac{1}{2}}

= (2^{\frac{1}{2}})^{2}

Apply exponent rule:

(a^{b})^{c} = a^{b c}

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

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

\frac{1}{2} \cdot 2

Multiply fractions:

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

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

Cancel the common factor:

2

= 1

= 2

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

6 \cdot \frac{1}{2}

Multiply fractions:

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

= \frac{1 \cdot 6}{2}

Multiply the numbers:

1 \cdot 6 = 6

= \frac{6}{2}

Divide the numbers:

\frac{6}{2} = 3

= 3

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

Add/Subtract the numbers:

2 - 3 = - 1

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

2^{2} = 4

= \frac{1}{4} - 1

Convert element to fraction:

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

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

Since the denominators are equal, combine the fractions:

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

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

- 1 \cdot 4 + 1 = - 3

- 1 \cdot 4 + 1

Multiply the numbers:

1 \cdot 4 = 4

= - 4 + 1

Add/Subtract the numbers:

- 4 + 1 = - 3

= - 3

= \frac{- 3}{4}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{3}{4}

= - \frac{3}{4}

Popular Examples

(600)/(sin(45))

\frac{600}{sin ( 4 5 ^{\circ} )}

sin(4(pi/4))

sin (4 (\frac{π}{4}))

(sin(20))/8

\frac{sin ( 2 0 ^{\circ} )}{8}

cos((6pi)/8)

cos (\frac{6 π}{8})

sin(159)

sin (15 9^{\circ})

Frequently Asked Questions (FAQ)

What is the value of sin^2(30)+sec^2(45)-6cos(60) ?
The value of sin^2(30)+sec^2(45)-6cos(60) is -3/4