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3 years ago

10

If θ is in Quadrant III and sinθ = -3/5, then cosθ = _____.

1 answer:

Nikolay [14]3 years ago

4 0

Because the angle omega is in QIII, the adjacent side lies to the left of the origin and thus is represented by a negative value. Since sin omega = -3/5, the opposite side is also negative. Use the Pythagorean Theorem to obtain the length of the adjacent side: 5^2 = (-3)^2 + x^2, or 25 = 9 + x^2, or x^2 = 16.

Solving for x: x = plus or minus 4. Since we are in QIII, let x = -4.

Then cos omega is opp / hyp, or -4/5.

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2 years ago

Use the given information to answer the following questions. center (3, -9, 3), radius 5 (a) Find an equation of the sphere with

lianna [129]

Answer: The equation of the sphere with the center and radius

$x^{2} +y^{2} +z^{2}-6 x+18 y-6 z+74=0$

b) The intersection of this sphere with the y z-plane the x- co-ordinate

is zero(i.e., x = 0 )

Step-by-step explanation:

a) The equation of the sphere having center (h,k,l) and radius r is

$(x-h)^{2} +(y-k)^2+(z-l)^2 = r^2$

Given center of the sphere (3, -9, 3) and radius 5

$(x-3)^{2}+(y+9)^2+(z-3)^2 = 5^2$

on simplification , we get solution

$x^{2} -6 x+9+y^{2} +18 y+81+z^{2}-6 z+9=25$

$x^{2} +y^{2} +z^{2}-6 x+18 y-6 z+74=0$

Final answer :-

$x^{2} +y^{2} +z^{2}-6 x+18 y-6 z+74=0$

b) The intersection of this sphere with the y z-plane the x- co-ordinate

is zero(i.e., x = 0 )

$y^{2} +z^{2}+18 y-6 z+74=0$

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3 years ago