What is the value of cos^2(-60) ?

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cos^2(-60)

cos^{2} (- 6 0^{\circ})

\frac{1}{4}

Decimal Notation

0.25

Solution steps

cos^{2} (- 6 0^{\circ})

Rewrite using trig identities:

cos (- 6 0^{\circ}) = \frac{1}{2}

cos (- 6 0^{\circ})

Use the following property:

cos (- x) = cos (x)

cos (- 6 0^{\circ}) = cos (6 0^{\circ})

= cos (6 0^{\circ})

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}

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

Simplify

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

(\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} = 4

= \frac{1}{4}

= \frac{1}{4}

arctan (\frac{43}{74})

30 cos (3 7^{\circ})

sin (6) π^{\circ}

- 5 cos (0)

sin (37. 5^{\circ}) cos (7. 5^{\circ})