How do you evaluate cos(53π6)?

For general form of cos(x), we will convert the value of x into the closest multiple of π2 and add or subtract a certain value α from that multiple of π2 to make it equal to x .Let’s assume that x=k× π2+α, k ∈ Z, |α|≤π2. For the given angle 53π6, we will express it as ⇒ 53π6=18×π2-π6.The value of k is even meaning that the trigonometric ratio remains cos.The position of the angle will be in the second quadrant. The angle completes the half-circle 9 times and then will come back π6.Hence, the sign becomes negative.The final form will be ⇒ cos(53π6)=cos(18×π2-π6). ⇒ cos(53π6)=-cos π6=-32

How do you evaluate cos(53π6)?

For general form of cos(x), we will convert the value of x into the closest multiple of π2 and add or subtract a certain value α from that multiple of π2 to make it equal to x .Let’s assume that x=k× π2+α, k ∈ Z, |α|≤π2. For the given angle 53π6, we will express it as ⇒ 53π6=18×π2-π6.The value of k is even meaning that the trigonometric ratio remains cos.The position of the angle will be in the second quadrant. The angle completes the half-circle 9 times and then will come back π6.Hence, the sign becomes negative.The final form will be ⇒ cos(53π6)=cos(18×π2-π6). ⇒ cos(53π6)=-cos π6=-32

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How do you evaluate $\cos (\frac{53 π}{6})$ ?

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\frac{\sqrt{3}}{2}

\frac{\sqrt{3}}{1}

\frac{\sqrt{5}}{2}

- \frac{\sqrt{3}}{2}

answer is D.

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Detailed Solution

For general form of

\cos (x)

, we will convert the value of

x

into the closest multiple of

\frac{π}{2}

and add or subtract a certain value α from that multiple of

\frac{π}{2}

to make it equal to

x

.
Let’s assume that

x = k \times \frac{π}{2} + α, k \in Z, | α | \leq \frac{π}{2} .

For the given angle 53π6, we will express it as
⇒

\frac{53 π}{6} = 18 \times \frac{π}{2} - \frac{π}{6}

.
The value of

k

is even meaning that the trigonometric ratio remains cos.
The position of the angle will be in the second quadrant. The angle completes the half-circle 9 times and then will come back