1. if cscθ=5/3 then secθ= a. 25/16 b. 5/4 c. 16/25 d. 4/5 2. simplify the expression (cos x) (sec x) - (sin2 x) a. cos x b. cos2 x c. sec2 x 3. if θ is in quadrant iv and sinθ=-5/4 then secθ= a. -13/12 b. -12/3 c. 12/13 d. 13/12

(1)

b.

(2)

b.

(3)

Step-by-step explanation:

(1)

we are given

we can use triangle method

we know that

csc=hyp/ opposite

so, hyp=5

opposite =3

now, we can find adjacent

we can use Pythagoras theorem

now, we can find sec

(2)

we are given

we can simplify it

now, we can replace 1 as sin^2x +cos^2x

we get

(3)

we are given

θ is in Quadrant IV

we know that

sin =opp/hyp

so, opp=5

hyp=13

now, we can use Pythagoras theorem

now, we can plug values

sec=hyp/adj

so, we get

problem:

f(x) = - 2/3x + 5; f(5/2)

substitute 5/2 in for x:

f(5/2) = -2/3(5/2) + 5

simplify the right side:

f(5/2) = -5/3 + 5

f(5/2) = 10/3

f(5/2) = 10/3

i hope this !