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Mathematics>Standard Multiple Choice

Read the following SAT test question and then click on a button to select your answer.

If θ=330°, what is the value of theta in radians?

A.3π/2
B.5π/3
C.7π/4
D.11π/6

答案和解析

答案：D

解析：

Recall that there are 2π radians in one revolution of a circle. There are also 360° in one revolution of a circle.

This leads us to the following conversion: 2π radians=360°

If we divide both sides by 360, we have 1°= π/180 radians.

We can use this factor to convert degrees to radians.

The conversion is performed below.

330°=330*1°=330π/180=11π/6

Alternatively, if we divide both sides of the equation 2π radians=360° by 12, we can conclude that π/6 radians=30°.

Since 330° is 11*30°, its measure in radians must be 11π/6.

Either way, we have the following: 330°=11π/6