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If 5,13,& 12 are the side lengths of a a triangle, then use the Cosine Rule, which is
a^(2)= b^(2) + c^(2) - 2bcCos(A)
Algebraically rearrange
Cos(A) -= [a^(2) - b^(2) - c^(2)] / [-2bc]
Substitute
Cos(A) = [5^(2) - 13^(2) - 12^(2)] / [-2(13)(12)]
Cos(A) = [25 - 169 - 144 ] / [-2(13)(12)]
Cos(A) = [-288] / [-312]
Cos(A) = 0.924076923 ( NB THe negatives(-) cancel out )
A = Cos^(-1) (0.924076923...)
A = 22.61986495... degrees.
NB This is the angular value of the angle formed by the intersection of the lines ,12, & ,13.
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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.
What is the tan of angle B in a 12 by 13 by 5 triangle?
In a triangle with sides measuring 12, 13, and 5, we can identify the angle opposite the side measuring 5 as angle B. To find the tangent of angle B, we use the formula ( \tan(B) = \frac{\text{opposite}}{\text{adjacent}} ). Here, the side opposite angle B is 5, and the adjacent side (which can be either of the other two sides depending on which angle we consider) is 12. Therefore, ( \tan(B) = \frac{5}{12} ).
What is the sin of angle B if the angles are 5 12 and 13?
This is a classic Pythagorean triangle. Although you have given the side lengths, you have NOT given a letter to correspond , with the given side. However, Let 12 be the adjacentr side (base) Let '5' be the opposite side ( perpendicular ) Let '13' by the hypotenuse. Sin(Angle) = opposite / hypotenuse = 5/13 Angle = Sin^(-1) 5/13 = 22.619... degrees. NB This is the angle between the hypotenuse and the base(adjacent) Now 'swopping' things around , we take the angle between the hypotenuse and the perpendicular (opposite) . This now becomes perpendicular(adjacent) and the base becomes the opposite. Hence Sin(angle) = 12/13 Angle = Sin^(-1) 12/13 = 67.380.... degrees. The angle at the 'top' of the triangle. Verification. ' 90 + 67.380... + 22.619... = 180 ( allow for calculator decimals).
Express cos4x sin3x in a series of sines of multiples of x?
The best way to answer this question is with the angle addition formulas. Sin(a + b) = sin(a)cos(b) + cos(a)sin(b) and cos(a + b) = cos(a)cos(b) - sin(a)sin(b). If you compute this repeatedly until you get sin(3x)cos(4x) = 3sin(x) - 28sin^3(x) + 56sin^5(x) - 32sin^7(x).
How do you confirm this trig identity?
sin^5 2x = 1/8 sin2x (cos(8x) - 4 cos(4x)+3)
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 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 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' 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.
If sin A 513 for angle A in Quadrant I find cos 2A?
To find ( \cos 2A ) using the given ( \sin A = \frac{5}{13} ), we first use the Pythagorean identity to find ( \cos A ). Since ( \sin^2 A + \cos^2 A = 1 ), we have ( \cos^2 A = 1 - \left(\frac{5}{13}\right)^2 = 1 - \frac{25}{169} = \frac{144}{169} ). Thus, ( \cos A = \frac{12}{13} ). Using the double angle formula ( \cos 2A = 2\cos^2 A - 1 ), we get ( \cos 2A = 2\left(\frac{12}{13}\right)^2 - 1 = 2 \cdot \frac{144}{169} - 1 = \frac{288}{169} - \frac{169}{169} = \frac{119}{169} ).
What is the exact ratio of all 6 trig functions when p is a point on a circle at 5 -12?
sin = -12/13 cos = 5/12 tan = -5/12 cosec = -13/12 sec = 12/5 cotan = -12/5
What is the sin of angle A 5 13 12?
The dimensions given fits that of a right angle triangle and sin^-1(12/13) = 67.38 degrees
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)
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.
What is the tan of angle B in a 12 by 13 by 5 triangle?
In a triangle with sides measuring 12, 13, and 5, we can identify the angle opposite the side measuring 5 as angle B. To find the tangent of angle B, we use the formula ( \tan(B) = \frac{\text{opposite}}{\text{adjacent}} ). Here, the side opposite angle B is 5, and the adjacent side (which can be either of the other two sides depending on which angle we consider) is 12. Therefore, ( \tan(B) = \frac{5}{12} ).
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 sin of angle B if the angles are 5 12 and 13?
This is a classic Pythagorean triangle. Although you have given the side lengths, you have NOT given a letter to correspond , with the given side. However, Let 12 be the adjacentr side (base) Let '5' be the opposite side ( perpendicular ) Let '13' by the hypotenuse. Sin(Angle) = opposite / hypotenuse = 5/13 Angle = Sin^(-1) 5/13 = 22.619... degrees. NB This is the angle between the hypotenuse and the base(adjacent) Now 'swopping' things around , we take the angle between the hypotenuse and the perpendicular (opposite) . This now becomes perpendicular(adjacent) and the base becomes the opposite. Hence Sin(angle) = 12/13 Angle = Sin^(-1) 12/13 = 67.380.... degrees. The angle at the 'top' of the triangle. Verification. ' 90 + 67.380... + 22.619... = 180 ( allow for calculator decimals).
