How would you work out the coordinates of the points?

The diagram shows the curve with equation y = cos (x - 2π/3), -2π < x < 2π. Write down the coordinates of the points at which the curve meets the coordinate axes.

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Apr 10, 2020 1:26 pm

How would you work out the coordinates of the points?

The diagram shows the curve with equation y = cos (x - 2π/3), -2π < x < 2π. Write down the coordinates of the points at which the curve meets the coordinate axes.

2 Replies

Apr 10, 2020 3:11 pm

Hi there

Solve it exactly how you would, of course -2pi < x < 2pi is the same as -360 < x < 360

The coordinate axes intersection is when x = 0 and when y = 0

so the easiets to find out is the y intercept

y = cos (x - 2pi/3)

plug in x = o

y = cos ( 0 - 2pi/3)

put your calculator in radians mode(menu -> 2 -> 2) then literally write cos (-2pi/3) and thats the y value

then for x axes intersection plug y = 0

0 = cos ( x - 2pi/3)

to get x, to cos inverse of 0

cos ( x - 2pi/3) = 0

x - 2pi/3 = cos^-1(0) = -270, -90, 90 and 270

But of course, turn that into radians instead of degrees

=================

so x - 2pi/3 = -270 degrees

which means x - 2pi/3 = -3pi/2

so x = -3pi/2 + 2pi/3 = **-5pi/6**

================

x - 2pi/3 = -90 degrees

which means x - 2pi/3 = -pi/2

so x = -pi/2 + 2pi/3 = **-pi/6**

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same for positive 90 degrees and 270 degrees solutions

Apr 10, 2020 5:20 pm

Thank you

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