INsanely Hard Question

Question

The angle θ satisfies cos(θ) = 1/4 and sin(θ) < 0

Find the value of sin(θ + pi/2)

Find the value of sin(pi − θ)

Show all work and explain your reasoning

Answer 1

Since cosθ>0 and sinθ<0, θ lies in quadrant 4.

 

cosθ=1/4   sinθ = -√[1 - cos²θ] = -√(15)/4 

 

sin(θ+π/2) = sinθcos(π/2) + cosθsin(π/2) = sinθ(0) + cosθ(1)

 

                                                                             = 1/4

 

sin(π - θ) = sinπcosθ - cosπsinθ = (0)cosθ - (-1)sinθ

 

                                                        = sinθ = -√(15)/4

Answer 2

I am assuming that you know that Sin (pi/2 +8) = cos 8 for all values of angle 8 

so your first ans will be cos theta which is given to be 1/4

 

and sin(pi -8) = sin 8 so your second ans will be sin 8 .plz excuse me for printing 8 for every value of theta because I dont know how to type special characters

 

since sin 8 is given to be negative  so it should be -sqroot 15/4