Question

If csc theta = -2.06, find sec(theta-pi/2)

Find the exact value
sin pi/ 18cos pi/9 + cos pi/18sin pi/ 9


Please help me soon, i dont need an explanation but it would be very helpful or if you know a website that can help me i will be very appreciative!

Answer 1

a) sec (θ -π/2) = co secθ

b)
`sin((\pi )/(18) ) cos ((\pi )/(9))+ cos((\pi )/(18) ) sin ((\pi )/(9) )=(1)/(2)`

Explanation:

a)

Given co sec θ = -2.06

sec (θ -π/2) = sec(π/2 -θ) = co secθ

b)

we will use formula

sin A cos B + Cos A sin B = sin(A+B)

Given
`sin((\pi )/(18) ) cos ((\pi )/(9))+ cos((\pi )/(18) ) sin ((\pi )/(9) )`

=
`Sin((\pi )/(18) +(\pi )/(9) )`

=
`sin((\pi+2\pi )/(18) ) = sin((3\pi )/(18))`

=
`sin((\pi )/(6))`

=
`(1)/(2)`