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The cosine of 15 degrees can be calculated using the cosine subtraction formula: ( \cos(15^\circ) = \cos(45^\circ - 30^\circ) ). This gives us ( \cos(15^\circ) = \cos 45^\circ \cos 30^\circ + \sin 45^\circ \sin 30^\circ ). Plugging in the known values, ( \cos 45^\circ = \frac{\sqrt{2}}{2} ), ( \cos 30^\circ = \frac{\sqrt{3}}{2} ), ( \sin 45^\circ = \frac{\sqrt{2}}{2} ), and ( \sin 30^\circ = \frac{1}{2} ), we find that ( \cos 15^\circ = \frac{\sqrt{6} + \sqrt{2}}{4} ).
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How do I find the product z1z2 if z1 5(cos20 plus isin20) and z2 8(cos15 plus isin15)?
Like normal expansion of brackets, along with: cos(A + B) = cos A cos B - sin A sin B sin(A + B) = sin A cos B + cos A sin B 5(cos 20 + i sin 20) × 8(cos 15 + i sin 15) = 5×8 × (cos 20 + i sin 20)(cos 15 + i sin 15) = 40(cos 20 cos 15 + i sin 15 cos 20 + i cos 15 sin 20 + i² sin 20 sin 15) = 40(cos 20 cos 15 - sin 20 cos 15 + i(sin 15 cos 20 + cos 15 sin 20)) = 40(cos(20 +15) + i sin(15 + 20)) = 40(cos 35 + i sin 35)
Sin 15 plus cos 105 equals?
Sin 15 + cos 105 = -1.9045
What is the cosine of 15 degrees?
cos(15 deg) = 0.9659, approx.
What is the angle of the moon?
The rate at which the lit portion of the moon moves per hour changes with latitude. The formula for finding the average rate of rotation per hour is: 15°cos(latitude). At the equator the equation would be 15°cos(0°)= 15° per hour.
What is sin23A minus sin7A upon sin2A plus sin14A if A equals pi upon 21?
Using the identity, sin(X)+sin(Y) = 2*sin[(x+y)/2]*cos[(x-y)/2] the expression becomes {2*sin[(23A-7A)/2]*cos[(23A+7A)/2]}/{2*sin[(2A+14A)/2]*cos[(2A-14A)/2]} = {2*sin(8A)*cos(15A)}/{2*sin(8A)*cos(-6A)} = cos(15A)/cos(-6A)} = cos(15A)/cos(6A)} since cos(-x) = cos(x) When A = pi/21, 15A = 15*pi/21 and 6A = 6*pi/21 = pi - 15pi/21 Therefore, cos(6A) = - cos(15A) and hence the expression = -1.
How do I find the product z1z2 if z1 5(cos20 plus isin20) and z2 8(cos15 plus isin15)?
Like normal expansion of brackets, along with: cos(A + B) = cos A cos B - sin A sin B sin(A + B) = sin A cos B + cos A sin B 5(cos 20 + i sin 20) × 8(cos 15 + i sin 15) = 5×8 × (cos 20 + i sin 20)(cos 15 + i sin 15) = 40(cos 20 cos 15 + i sin 15 cos 20 + i cos 15 sin 20 + i² sin 20 sin 15) = 40(cos 20 cos 15 - sin 20 cos 15 + i(sin 15 cos 20 + cos 15 sin 20)) = 40(cos(20 +15) + i sin(15 + 20)) = 40(cos 35 + i sin 35)
Cos 195 degree use the trigonometry functions of quadrantal angles and special to find the exact value?
cos(195) = cos(180 + 15) = cos(180)*cos(15) - sin(180)*sin(15) = -1*cos(15) - 0*sim(15) = -cos(15) = -cos(60 - 45) = -[cos(60)*cos(45) + sin(60)*sin(45)] = -(1/2)*sqrt(2)/2 - sqrt(3)/2*sqrt(2)/2 = - 1/4*sqrt(2)*(1 + sqrt3) or -1/4*[sqrt(2) + sqrt(6)]
Sin 15 plus cos 105 equals?
Sin 15 + cos 105 = -1.9045
What is the exact value of cos 15?
It is: cos(15) = (sq rt of 6+sq rt of 2)/4
What is the cosine of 15 degrees?
cos(15 deg) = 0.9659, approx.
Int cos 10x cos 15x dx?
There is some kind of formula here, half angle, or some such that I forget, but I do remember the algorithm. So...,int[cos(10X)cos(15X)] dxsince this is multiplicative, switch it aroundint[cos(15X)cos(10X)] dxint[cos(15X - 10X)/2(15 -10) + cos(15X + 10X)/2(15 + 10)] dxint[cos(5X)/10 + cos(25X)/50] dx= 1/10sin(5X) + 1/50sin(25X) + C=========================
What is the exact value of cos theta if csc theta -4 with theta in quadrant III?
csc θ = 1/sin θ → sin θ = -1/4 cos² θ + sin² θ = 1 → cos θ = ± √(1 - sin² θ) = ± √(1 - ¼²) = ± √(1- 1/16) = ± √(15/16) = ± (√15)/4 In Quadrant III both cos and sin are negative → cos θ= -(√15)/4
What is the angle of the moon?
The rate at which the lit portion of the moon moves per hour changes with latitude. The formula for finding the average rate of rotation per hour is: 15°cos(latitude). At the equator the equation would be 15°cos(0°)= 15° per hour.
What is the lowest common multiple of 4 6 and 15?
4, 6 and 15 or 46 and 15 cos 4,6 and 15 LCM is 360 (4 x 6 x 15)
What can my girlfriend and i do that's taking it further than making out apart from sex cos we both know were not ready cos were 15?
look at each other and have a friendly chat about the weather
What is sin23A minus sin7A upon sin2A plus sin14A if A equals pi upon 21?
Using the identity, sin(X)+sin(Y) = 2*sin[(x+y)/2]*cos[(x-y)/2] the expression becomes {2*sin[(23A-7A)/2]*cos[(23A+7A)/2]}/{2*sin[(2A+14A)/2]*cos[(2A-14A)/2]} = {2*sin(8A)*cos(15A)}/{2*sin(8A)*cos(-6A)} = cos(15A)/cos(-6A)} = cos(15A)/cos(6A)} since cos(-x) = cos(x) When A = pi/21, 15A = 15*pi/21 and 6A = 6*pi/21 = pi - 15pi/21 Therefore, cos(6A) = - cos(15A) and hence the expression = -1.
What is cos square?
Cos times Cos
