What is the value of sin^2(30)+sec^2(45) ?

The value of sin^2(30)+sec^2(45) is 9/4

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sin^2(30)+sec^2(45)

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

\frac{9}{4}

Decimal Notation

2.25

Solution steps

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

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

Simplify

(\frac{1}{2})^{2} + (2)^{2} : \frac{9}{4}

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

2^{2} = 4

= \frac{1}{4} + 2

Convert element to fraction:

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

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

2 \cdot 4 + 1 = 9

2 \cdot 4 + 1

Multiply the numbers:

2 \cdot 4 = 8

= 8 + 1

Add the numbers:

8 + 1 = 9

= 9

= \frac{9}{4}

= \frac{9}{4}

0.4 sin (π \cdot 5)

csc (23 0^{\circ}) - cot (24 5^{\circ})

arctan (0.656)

825 cos (6 0^{\circ}) - 1746.3286 cos (39.2 9^{\circ})

19 \cdot sin (3 5^{\circ})

What is the value of sin^2(30)+sec^2(45) ?
The value of sin^2(30)+sec^2(45) is 9/4