What is the value of sin^2(30)+cos^2(60) ?

The value of sin^2(30)+cos^2(60) is 1/2

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sin^2(30)+cos^2(60)

sin^{2} (3 0^{\circ}) + cos^{2} (6 0^{\circ})

\frac{1}{2}

Decimal Notation

0.5

Solution steps

sin^{2} (3 0^{\circ}) + cos^{2} (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:

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

Simplify

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

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

Add similar elements:

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

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

Multiply fractions:

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

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

Multiply the numbers:

1 \cdot 2 = 2

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

Cancel the common factor:

2

= \frac{1}{2}

= \frac{1}{2}

\frac{tan ( 7 8 ^{\circ} ) - tan ( 1 8 ^{\circ} )}{1 + tan ( 7 8 ^{\circ} ) tan ( 1 8 ^{\circ} )}

sec (\frac{π}{8}) - \frac{1}{( \frac{π}{8} ) ^{3}} + 5

\frac{3.7}{cos ( 6 4 ^{\circ} )}

sin (2 (π))

arccos (\frac{4.6}{8.6})

What is the value of sin^2(30)+cos^2(60) ?
The value of sin^2(30)+cos^2(60) is 1/2