Question

What is the reference angle for `(-15pi)/6`?

Answer 1

`pi/2`

Explanation:

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Definition

`"Reference angle of an angle is the smallest angle that we"`
`"can make from where the angle ends to the x-axis"`

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`color(blue)((-15pi)/6`

Let's convert it from radians to degrees

`rarr(-15pi)/6=(-15(180))/6`

`rarr(-15*cancel180^30)/cancel6^1`

`rarr-15*30`

`rArr-450^circ`

We need to find the reference angle of `-450^circ`

Let's mark the angle

From this we can say

`color(blue)(90^circ` `"is the reference angle of "` `color(red)(-450^circ`

As the smallest angle that we can make from `"x-axis"` is `90^circ`

Convert `90^circ` to radian measure using the formula

`color(brown)("Radians"="Degrees"*pi/180`

`rarr90^circ*pi/180` `"radians"`

`rarr(90^circ*pi)/180` `"radians"`

`rarr(cancel90^1*pi)/cancel180^2` `"radians"`

`color(green)(rArrpi/2` #color (green)("radians"#

For better understanding of reference angles,

Watch this video