Given that cos 13pi/18=sin y, first express 13pi/18 as a sum of pi/2 and an angle, and then apply a trigonometric identitiy to determine the measure of angle y

Answer 1

come on, man. This is 4th grade addition of fractions.
13/18 = 9/18 + 5/18
now, cos(13π/18) = cos(π/2) cos(5π/18) - sin(π/2) sin(5π/18) = -sin(5π/18)
so y = -5π/18
If you want a positive angle, just add 2π to that.

Answer 2

13 π / 18 = π / 2 + θ

Subtract π / 2 to both sides

13 π / 18 - π / 2 = θ

13 π / 18 - 9 π / 18 = θ

4 π / 18 = θ

2 ∙ 2 π / 2 ∙ 9 = θ

2 π / 9 = θ

θ = 2 π / 9

13 π / 18 = π / 2 + 2 π / 9

Use identity:

cos ( π / 2 + θ ) = - sin ( θ )

cos ( 13 π / 18 ) = cos ( π / 2 + 2 π / 9 ) = - sin ( 2 π / 9 )

Now:

cos ( 13 π / 18 ) = sin ( y )

- sin ( 2 π / 9 ) = sin ( y )

sin ( y ) = - sin ( 2 π / 9 )

The solutions are:

y = - 2 π / 9 + 2 π n
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Since:

sin ( π + θ ) = - sin( θ )

sin ( π + 2 π / 9 ) = - sin ( 2 π / 9 )

sin ( 9 π / 9 + 2 π / 9 ) = - sin ( 2 π / 9 )

sin ( 11 π / 9 ) = - sin ( 2 π / 9 )

y = 11 π / 9 + 2 π n
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Answer 3

oops. How ever did I get 5/18?
Luckily, it was Bosnian for the save!