cos(a)cos(b)-sin(a)sin(b)=cos(a+b)
a=7pi/12 and b=pi/6
a+b = 7pi/12 + pi/6 = 7pi/12 + 2pi/12 = 9pi/12
We want to find cos(9pi/12)
cos(9pi/12) = cos(3pi/4)
cos(3pi/4)= cos(pi-pi/4)
cos(pi)cos(pi/4)-sin(pi)sin(pi/4)
cos(pi)=-1
sin(pi)=0
cos(pi/4) = √2/2
sin(pi/4) =√2/2
cos(pi)cos(pi/4)-sin(pi)sin(pi/4) = - cos(pi/4) = -√2/2
π/6
7pi liters
1.75
Okay so you know that the area is equal to 7. So: A=7 the area for a circle is A= (pi)r2 where A is the area. so 7=(pi)r2 solve for r 7/(pi)=r2 sqrt (7/(pi))=r rationalize it [sqrt(7pi)]/(pi) if you double the radius you get the diameter. 2r=d d=2[sqrt(7pi)]/(pi)
Since 90 degrees is pi/2 radians, 70 degrees would be (7/9*pi/2)=7pi/18 radians.
( 2 x pi x 7)/12 = 7pi/6 = 3ft 8 in
The answer is 7pi radians, or 7*180° = 1260° (N-2)pi radians, or (N-2)*180° N is the number of sides on the polygon; Sum of interior angles formula
7/9=14/18=28/36=70/90Essentially multiply the top and bottom by the same number, and it's the same.7pi/9pi=7e/9e=7i/9i7/9=(7 times some number)/(9 times the same number)
cosx + sinx = 0 when sinx = -cosx. By dividing both sides by cosx you get: sinx/cosx = -1 tanx = -1 The values where tanx = -1 are 3pi/4, 7pi/4, etc. Those are equivalent to 135 degrees, 315 degrees, etc.
There are an infinite number of answers.For example:.07 x 100.007 x 1000.0007 x 1000049 x 1/7350 x 1/50(-1) x (-7)(square root of 7) x (square root of 7)7pi x 1/pi
sinx-cosx=0 --> move cosx to opposite side sinx=cosx --> square both sides sin2x=cos2x --> use pythagorean identities for (cos2x=1-sin2x) sin2x=1-sin2x --> add sin2x to both sides of equation 2sin2x=1 --> divide both sides by 2 sin2x=1/2 --> take the square root of both sides sinx= +/- (square root of 2)/2 or .7071 If giving answers in radians --> answer appears in all four quadrants, so answer would be (pi/4 + piN/2). Other answers would be (3pi/4 + piN/2), (5pi/4 + piN/2), and (7pi/4 + piN/2). Check for extraneous solutions: The answers in the first and third quadrant are extraneous. Therefore, your answer is (3pi/4 + piN), because every pi, an answer occurs. In one trip around the quadrants, both 3pi/4 and 7pi/4 are answers.
Find all solutions of z4 = -8i.Recall:z = a + bi, the complex formz = |z|(cos θ + i sin θ), the polar coordinate formSo we can write:z4 = [|z|(cos θ + i sin θ)]4 = |z|4(cos 4θ + i sin 4θ); -8i = 8(0 - i), and we have|z|4(cos 4θ + i sin 4θ) = 8(0 - i).Thus, |z|4 = 8, so |z|= 81/4.The angle θ for z must satisfy cos 4θ = 0 and sin 4θ = -1.Consequently, 4θ = 3pi/2 + 2npi for an integer n, so that θ = 3pi/8 + npi/2.The different values of θ obtained where 0 ≤ θ ≤ 2pi are:n = 0, θ = 3pi/8 (1st quadrant)n = 1, θ = 3pi/8 + pi/2 = 7pi/8 (2nd quadrant)n = 2, θ = 3pi/8 + pi = 11pi/8 ( 3rd quadrant)n = 3, θ = 3pi/8 + 3pi/2 = 15pi/8 (4th quadrant))Thus the solutions of z4 = -8i are(81/4)(cos 3pi/8 + i sin 3pi8) ≈ 0.6435942529 + 1.553773974 i(81/4)(cos 7pi/8 + i sin 7pi/8) ≈ -1.553773974 + 0.6435942529 i(81/4)(cos 11pi/8 + i sin 11pi/8) ≈ -0.6435942529 - 1.553773974 i(81/4)(cos 15pi/8 + i sin 15pi/8) ≈ 1.553773974 - 0.6435942529 i