What is the value of sec^2(570) ?

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sec^2(570)

sec^{2} (57 0^{\circ})

\frac{4}{3}

Decimal Notation

1.33333 \dots

Solution steps

sec^{2} (57 0^{\circ})

sec (57 0^{\circ}) = sec (21 0^{\circ})

sec (57 0^{\circ})

Rewrite

57 0^{\circ}

36 0^{\circ} + 21 0^{\circ}

= sec (36 0^{\circ} + 21 0^{\circ})

Apply the periodicity of

sec

sec (x + 36 0^{\circ}) = sec (x)

sec (36 0^{\circ} + 21 0^{\circ}) = sec (21 0^{\circ})

= sec (21 0^{\circ})

= sec^{2} (21 0^{\circ})

Rewrite using trig identities:

tan^{2} (3 0^{\circ}) + 1

sec^{2} (21 0^{\circ})

Use the Pythagorean identity:

sec^{2} (x) = tan^{2} (x) + 1

= tan^{2} (21 0^{\circ}) + 1

tan (21 0^{\circ}) = tan (3 0^{\circ})

tan (21 0^{\circ})

Rewrite

21 0^{\circ}

18 0^{\circ} + 3 0^{\circ}

= tan (18 0^{\circ} + 3 0^{\circ})

Apply the periodicity of

tan

tan (x + 18 0^{\circ}) = tan (x)

tan (18 0^{\circ} + 3 0^{\circ}) = tan (3 0^{\circ})

= tan (3 0^{\circ})

= tan^{2} (3 0^{\circ}) + 1

= tan^{2} (3 0^{\circ}) + 1

Use the following trivial identity:

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

tan (3 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}

= \frac{3}{3}

= (\frac{3}{3})^{2} + 1

Simplify

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

(\frac{3}{3})^{2} + 1

(\frac{3}{3})^{2} = \frac{1}{3}

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

Apply exponent rule:

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

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

(3)^{2} : 3

Apply radical rule:

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

= (3^{\frac{1}{2}})^{2}

Apply exponent rule:

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

= 3^{\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

= 3

= \frac{3}{3 ^{2}}

Cancel the common factor:

3

= \frac{1}{3}

= \frac{1}{3} + 1

Convert element to fraction:

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

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

Since the denominators are equal, combine the fractions:

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

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

1 \cdot 3 + 1 = 4

1 \cdot 3 + 1

Multiply the numbers:

1 \cdot 3 = 3

= 3 + 1

Add the numbers:

3 + 1 = 4

= 4

= \frac{4}{3}

= \frac{4}{3}

8 cos (6 0^{\circ})

cos (\frac{π}{1})

cos (25 0^{\circ})

cos (2 (\frac{π}{2}))

arcsin (\frac{3}{2})