Answer:
Part A: if cosθ = 4/5 and sinθ < 0, then
secθ = 5/4
sinxθ = 3
tanθ = 15/4, cotθ = 12/5, cscx = 1/3
Step-by-step explanation:
Remember, secθ = 1/4/5 --> 1/4 *5/1 = 5/4
sinx, cscx, cotx, and tanx will be negative because since sinθ < 0 and cosθ is positive, this means that the quadrant will be in quadrant 4
To find these values, we have to use the pythagorean identities
cosx = adj/hyp, sinx = opp/hyp, and tanx = adj/opp
Since 4 is the value of the adjacent side, and we know that x² + 4² = 5².
x² + 16 = 25 ---> x² = 9--> x =3.
Since the value of the opposite side equals 3, and sinx = y, y = 3. Now we can find the rest of our trig values.
Remember that cosθ = x and sinθ = y
tanθ = y/x, cotθ = x/y, secθ = 1/x, cscx = 1/y.
So, since cosθ = 4/5 and sinθ = 3,
tanθ = 15/4, cotθ = 12/5, cscx = 1/3
