Use an identity to write the expression as a single trigonometric function value or as a single number.
$\frac{1}{6} - \frac{1}{3} \sin^{2} {35.9}^{\circ}$
$\frac{1}{6} - \frac{1}{3} \sin^{2} {35.9}^{\circ} =$
(Type an exact answer, using radicals as needed. Do not include the degree symbol in your answer.)

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Final Answer: The expression $\frac{1}{6} - \frac{1}{3} \sin^{2} {35.9}^{\circ}$ simplifies to $0.052$ .

Steps

Step 1 ：Given the expression $\frac{1}{6} - \frac{1}{3} \sin^{2} {35.9}^{\circ}$

Step 2 ：We can use the Pythagorean identity in trigonometry, which states that $\sin^{2} (x) + \cos^{2} (x) = 1$ . From this identity, we can express $\sin^{2} (x)$ as $1 - \cos^{2} (x)$ .

Step 3 ：Substituting this into the given expression, we get $\frac{1}{6} - \frac{1}{3} (1 - \cos^{2} ({35.9}^{\circ}))$

Step 4 ：Converting the angle to radians, we get approximately 0.627 radians.

Step 5 ：Calculating the cosine of this angle, we get approximately 0.810.

Step 6 ：Substituting this value back into the expression, we get approximately 0.052.

Step 7 ：Final Answer: The expression $\frac{1}{6} - \frac{1}{3} \sin^{2} {35.9}^{\circ}$ simplifies to $0.052$ .

Use an identity to write the expression as a single trigonometric function value or as a single number.16−13sin2⁡35.9∘16−13sin2⁡35.9∘=(Type an exact answer, using radicals as needed. Do not include the degree symbol in your answer.)

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