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Popular >

225^{sin(30)}

Solution

22 5^{s i n (3 0^{\circ})}

Solution

15

Solution steps

22 5^{s i n (3 0^{\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}

= 22 5^{\frac{1}{2}}

Simplify

22 5^{\frac{1}{2}} : 15

22 5^{\frac{1}{2}}

Factor the number:

225 = 1 5^{2}

= (1 5^{2})^{\frac{1}{2}}

Apply exponent rule:

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

(1 5^{2})^{\frac{1}{2}} = 1 5^{2 \cdot \frac{1}{2}} = 15

= 15

= 15

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0.71 (9.8) sin (1 0^{\circ})

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Frequently Asked Questions (FAQ)

What is the value of 225^{sin(30)} ?
The value of 225^{sin(30)} is 15