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 seventy-nine million four hundred ninety-three thousand six hundred forty-eight

Interesting facts

179493648 has 128 divisors, whose sum is 1212962688
The reverse of 179493648 is 846394971
Previous prime number is 3023

Basic properties

Is Prime? no
Number parity even
Number length 9
Sum of Digits 51
Digital Root 6

Name

Name	six hundred forty-eight million seven hundred thirty-seven thousand five

Interesting facts

648737005 has 8 divisors, whose sum is 681471360
The reverse of 648737005 is 500737846
Previous prime number is 47

Basic properties

Is Prime? no
Number parity odd
Number length 9
Sum of Digits 40
Digital Root 4

Name

Name	one billion four hundred three million six hundred three thousand eight hundred eighteen

Interesting facts

1403603818 has 8 divisors, whose sum is 2105953380
The reverse of 1403603818 is 8183063041
Previous prime number is 3929

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 34
Digital Root 7

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Find the Value Using the Unit Circle cos((5pi)/2)

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Solve the System of Inequalities 10x+7y=180 , 10x-11y=0