What is the value of 3sin^2(45)+4cos^2(45) ?

The value of 3sin^2(45)+4cos^2(45) is 7/2

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3sin^2(45)+4cos^2(45)

3 sin^{2} (4 5^{\circ}) + 4 cos^{2} (4 5^{\circ})

\frac{7}{2}

Decimal Notation

3.5

Solution steps

3 sin^{2} (4 5^{\circ}) + 4 cos^{2} (4 5^{\circ})

Use the following trivial identity:

sin (4 5^{\circ}) = \frac{2}{2}

sin (4 5^{\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{2}{2}

Use the following trivial identity:

cos (4 5^{\circ}) = \frac{2}{2}

cos (4 5^{\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{2}{2}

= 3 (\frac{2}{2})^{2} + 4 (\frac{2}{2})^{2}

Simplify

3 (\frac{2}{2})^{2} + 4 (\frac{2}{2})^{2} : \frac{7}{2}

3 (\frac{2}{2})^{2} + 4 (\frac{2}{2})^{2}

Add similar elements:

3 (\frac{2}{2})^{2} + 4 (\frac{2}{2})^{2} = 7 (\frac{2}{2})^{2}

= 7 (\frac{2}{2})^{2}

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

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

Apply exponent rule:

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

= \frac{( 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

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

Cancel the common factor:

2

= \frac{1}{2}

= 7 \cdot \frac{1}{2}

Multiply fractions:

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

= \frac{1 \cdot 7}{2}

Multiply the numbers:

1 \cdot 7 = 7

= \frac{7}{2}

= \frac{7}{2}

sin (\frac{π}{5}) cos (\frac{2 π}{15}) + cos (\frac{π}{5}) sin (\frac{2 π}{15})

\frac{0.02}{tan ( 20 7 ^{\circ} )}

e^{\frac{3 π}{2}} sin (\frac{3 π}{2})

sec (3 1^{\circ})

arccos (\frac{- 4}{21})

What is the value of 3sin^2(45)+4cos^2(45) ?
The value of 3sin^2(45)+4cos^2(45) is 7/2