Find the value of sec (θ)for an angle θ in standard position with a terminal Ray that passes through the point (4, -3)

B

Step-by-step explanation:

See the attachment.

We know that since the point is (4, -3), it's in the fourth quadrant. Drop a perpendicular from the point to the x-axis and produce a right triangle. This triangle has opposite as length -3 and adjacent as 4. We need to find the hypotenuse, so use the Pythagorean Theorem:

c² = a² + b²

c² = (-3)² + 4² = 9 + 16 = 25

c = 5

Secant is hypotenuse over adjacent, so we have:

sec(θ) = 5/4

The answer is B.

b

Step-by-step explanation:

Please see attached picture for full solution.

there are many solutions.

step-by-step explanation:

step 1: simplify both sides of the equation.

4x+6=4x^2+10x−4

step 2: subtract 4x^2+10x-4 from both sides.

4x+6−(4x^2+10x−4)=4x^2+10x−4−(4x^2+10x−4)

−4x^2−6x+10=0

step 3: factor left side of equation.

−2(2x+5)(x−1)=0

step 4: set factors equal to 0.

x=-5/2 or x=1

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4