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How do you calculate cos squared theta equals one minus twelve thirteenths squared?
Writing x instead of theta, cos2x = 1 - (12/13)2 = 1 - 144/169 = 25/169 = (5/13)2 So cos(x) = ± 5/13 so that x = cos-1(5/13) or cos-1(-5/13) And then, depending on the range of x, you have solutions for x. A calculator will only give you the principal solutions, though.
I have magnitude and angle how can find a b and a Dot b a 3 angle 45 b 5 angle 90 Find A B A dot B?
a = 3/sqrt(2)*i + 3/sqrt(2)*jb = 5ja.b = |a|*|b|*cos(q)= 3*5*cos(45) = 15/sqrt(2)
How do you find hypotenuse c angle a equals 30 deg side b equals 5 mm?
To find the hypotenuse with angle a and side b, we use the identity below:cos(a) = b/cWe have a and b, and to find c, we multiply both sides by c and divide both sides by cos(a):c = b/cos(a)c = 5/cos(30)c = 32.41460617mm
What is the sin of angle a if bc is 5 ba is 13 and ca is 12?
5/13 = 0.3846 (to 4 dp)
What is the approximate size of the smallest angle of a triangle whose sides are 4 5 and 8?
Why approximate? I will show you what you should know being in the trig section. Law of cosines. Degree mode!! a = 4 (angle opposite = alpha) b = 5 ( angle opposite = beta) c = 8 ( angle opposite = gamma ) a^2 = b^2 + c^2 - 2bc cos(alpha) 4^2 = 5^2 + 8^2 - 2(5)(8) cos(alpha) 16 = 89 - 80 cos(alpha) -73 = -80 cos(alpha) 0.9125 = cos(alpha) arcos(0.9125) = alpha alpha = 24.15 degrees ------------------------------ b^2 = a^2 + c^2 - 2bc cos(beta) 5^2 = 4^2 + 8^2 - 2(4)(8) cos(beta) 25 = 80 - 64 cos(beta) -55 = -64 cos(beta) 0.859375 = cos(beta) arcos(0.859375) = beta beta = 30.75 degrees --------------------------------- Now to find gamma, subtract from 180 degrees 180 - 24.15 - 30.75 = 125.1 degrees alpha = 24.15 degrees ( subject to rounding, but all add to 180 degrees ) beta = 30.75 degrees gamma = 125.1 degrees now you see the smallest, the angle opposite the a side, which is 4 ( be in degree mode!!)
What is cos of angle a with a hypotenuse of 13 and adjacent of 5 and a opposite of 12?
Cos(angle) = adjacent / hypotenuse. Cos(a) = a/h Substitute Cos(X) = 5/13 = 0.384615... A = Cos^*-1( 0.384615 .... A = 67.38013505... degrees.
What is the cos of angle a if the opposite is 5 the adjacent is 12 and the hypotenuse is 13?
It is: cos^-1(12/13) = 22.61986495 degrees
What is the cos of angle a 5 13 12?
It is: cos = adj/hyp and the acute angles for the given right angle triangle are 67.38 degrees and 22.62 degrees
What is the cos of angle A if the opposite is 3 and the adjacent is 4 and the hypotenuse is 5?
4/5
What is the cos of angle 'a' with the measurements 5 13 12?
Use Cosine Rule a^(2) = b^(2) + c^(2) - 2bcCosA Algebrically rearrange CosA = [a^(2) - b^(2) - c^(2)] / -2bc Substitute CosA = [13^(2) - 12^(2) - 5^(2)# / -2(12)(5) CosA = [ 169 - 144 - 25] / -120 Cos)A) = [0] / -120 CosA = 0 A = 90 degrees (the right angle opposite the hypotenuse)/ However, If 'A' is the angle between '12' & '13' then 'a' is the side '5' Hence (Notice the rearrangement of the numerical values). CosA = [5^(2) - 12^(2) - 13^(2) ] / -2(12)(13) CosA = [ 25 - 144 -169] / -312 CosA = [ -288[/-312 CosA = 288/312 A = Cos^(-1) [288/312] A = 22.61986495.... degrees.
How do you calculate cos squared theta equals one minus twelve thirteenths squared?
Writing x instead of theta, cos2x = 1 - (12/13)2 = 1 - 144/169 = 25/169 = (5/13)2 So cos(x) = ± 5/13 so that x = cos-1(5/13) or cos-1(-5/13) And then, depending on the range of x, you have solutions for x. A calculator will only give you the principal solutions, though.
I have magnitude and angle how can find a b and a Dot b a 3 angle 45 b 5 angle 90 Find A B A dot B?
a = 3/sqrt(2)*i + 3/sqrt(2)*jb = 5ja.b = |a|*|b|*cos(q)= 3*5*cos(45) = 15/sqrt(2)
How do you find hypotenuse c angle a equals 30 deg side b equals 5 mm?
To find the hypotenuse with angle a and side b, we use the identity below:cos(a) = b/cWe have a and b, and to find c, we multiply both sides by c and divide both sides by cos(a):c = b/cos(a)c = 5/cos(30)c = 32.41460617mm
What is the sin of angle a if bc is 5 ba is 13 and ca is 12?
5/13 = 0.3846 (to 4 dp)
What is the measure of x if the measure of angle abd is represented by 2x the measure of angle dbc is represented by 5x and the measure of angle abc is 91 degrees?
The answer is 13. x=13 13*5+13*2=91 Thank you.
What is the approximate size of the smallest angle of a triangle whose sides are 4 5 and 8?
Why approximate? I will show you what you should know being in the trig section. Law of cosines. Degree mode!! a = 4 (angle opposite = alpha) b = 5 ( angle opposite = beta) c = 8 ( angle opposite = gamma ) a^2 = b^2 + c^2 - 2bc cos(alpha) 4^2 = 5^2 + 8^2 - 2(5)(8) cos(alpha) 16 = 89 - 80 cos(alpha) -73 = -80 cos(alpha) 0.9125 = cos(alpha) arcos(0.9125) = alpha alpha = 24.15 degrees ------------------------------ b^2 = a^2 + c^2 - 2bc cos(beta) 5^2 = 4^2 + 8^2 - 2(4)(8) cos(beta) 25 = 80 - 64 cos(beta) -55 = -64 cos(beta) 0.859375 = cos(beta) arcos(0.859375) = beta beta = 30.75 degrees --------------------------------- Now to find gamma, subtract from 180 degrees 180 - 24.15 - 30.75 = 125.1 degrees alpha = 24.15 degrees ( subject to rounding, but all add to 180 degrees ) beta = 30.75 degrees gamma = 125.1 degrees now you see the smallest, the angle opposite the a side, which is 4 ( be in degree mode!!)
What is the angle of PQR whose coordinates are 5 9 and 14 -3 and 2 3 respectively thus forming a right angle triangle?
The angle of Q works out as: cos-1((6*square root of 5)/15) = 26.6 degrees to 1 decimal place
