Simplify sin(150)^2+cos(30)^2

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Trigonometry

$\sin^{2} (150) + \cos^{2} (30)$

Simplify each term.

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Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.

$\sin^{2} (30) + \cos^{2} (30)$

The exact value of $\sin (30)$ is $\frac{1}{2}$ .

${(\frac{1}{2})}^{2} + \cos^{2} (30)$

Apply the product rule to $\frac{1}{2}$ .

$\frac{1^{2}}{2^{2}} + \cos^{2} (30)$

One to any power is one.

$\frac{1}{2^{2}} + \cos^{2} (30)$

Raise $2$ to the power of $2$ .

$\frac{1}{4} + \cos^{2} (30)$

The exact value of $\cos (30)$ is $\frac{\sqrt{3}}{2}$ .

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

Apply the product rule to $\frac{\sqrt{3}}{2}$ .

$\frac{1}{4} + \frac{{\sqrt{3}}^{2}}{2^{2}}$

Rewrite ${\sqrt{3}}^{2}$ as $3$ .

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Rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

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

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{1}{4} + \frac{3^{\frac{1}{2} \cdot 2}}{2^{2}}$

Combine $\frac{1}{2}$ and $2$ .

$\frac{1}{4} + \frac{3^{\frac{2}{2}}}{2^{2}}$

Cancel the common factor of $2$ .

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Cancel the common factor.

$\frac{1}{4} + \frac{3^{\frac{2}{2}}}{2^{2}}$

Divide $1$ by $1$ .

$\frac{1}{4} + \frac{3^{1}}{2^{2}}$

Evaluate the exponent.

$\frac{1}{4} + \frac{3}{2^{2}}$

Raise $2$ to the power of $2$ .

$\frac{1}{4} + \frac{3}{4}$

Combine the numerators over the common denominator.

$\frac{1 + 3}{4}$

Add $1$ and $3$ .

$\frac{4}{4}$

Divide $4$ by $4$ .

$1$

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Name

Name	one hundred ninety-eight million three hundred two thousand six hundred thirty-one

Interesting facts

198302631 has 4 divisors, whose sum is 264403512
The reverse of 198302631 is 136203891
Previous prime number is 3

Basic properties

Is Prime? no
Number parity odd
Number length 9
Sum of Digits 33
Digital Root 6

Name

Name	three hundred fourteen million eight hundred seventy-six thousand two hundred ninety-six

Interesting facts

314876296 has 64 divisors, whose sum is 1215611712
The reverse of 314876296 is 692678413
Previous prime number is 3373

Basic properties

Is Prime? no
Number parity even
Number length 9
Sum of Digits 46
Digital Root 1

Name

Name	one billion three hundred ninety-nine million seven hundred seventy-six thousand six hundred sixty-six

Interesting facts

1399776666 has 32 divisors, whose sum is 2894309376
The reverse of 1399776666 is 6666779931
Previous prime number is 691

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 60
Digital Root 6

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