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

Answer:

a) sec (θ -π/2) =  co secθ

b) $sin(\frac{\pi }{18} ) cos (\frac{\pi }{9})+ cos(\frac{\pi }{18} ) sin (\frac{\pi }{9} )=\frac{1}{2}$

Step-by-step 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 $sin(\frac{\pi }{18} ) cos (\frac{\pi }{9})+ cos(\frac{\pi }{18} ) sin (\frac{\pi }{9} )$

                                                =  $Sin(\frac{\pi }{18} +\frac{\pi }{9} )$

                                                = $sin(\frac{\pi+2\pi }{18} ) = sin(\frac{3\pi }{18})$

                                                = $sin(\frac{\pi }{6})$

                                               =  $\frac{1}{2}$