What is the value of 5cos(540) ?

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5cos(540)

5 cos (54 0^{\circ})

- 5

Solution steps

5 cos (54 0^{\circ})

Rewrite using trig identities:

cos (54 0^{\circ}) = - 1

cos (54 0^{\circ})

cos (54 0^{\circ}) = cos (18 0^{\circ})

cos (54 0^{\circ})

Rewrite

54 0^{\circ}

36 0^{\circ} + 18 0^{\circ}

= cos (36 0^{\circ} + 18 0^{\circ})

Apply the periodicity of

cos

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

cos (36 0^{\circ} + 18 0^{\circ}) = cos (18 0^{\circ})

= cos (18 0^{\circ})

= cos (18 0^{\circ})

Use the following trivial identity:

cos (18 0^{\circ}) = (- 1)

cos (18 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}

= (- 1)

= - 1

= 5 (- 1)

Simplify

= - 5

csc (0.9)

arcsin (\frac{12}{11} sin (7 3^{\circ}))

sin (0.245)

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

cot (6 0^{\circ}) tan (3 0^{\circ}) + sec^{2} (4 5^{\circ}) sin (3 0^{\circ})