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Write 5cos(theta) – 2sin(theta) in the form Rcos(theta + alpha), where R and alpha are constants, R > 0 and 0 <=alpha < 2 π Give the exact value of R and give the value of alpha in radians to 3 decimal places.

Use the formula cos(A+B)=cosAcosB-sinAsinB, Rcos(theta+alpha)=Rcos(alpha)cos(theta)-Rsin(alpha)sin(theta)5=Rcos(alpha)2=Rsin(alpha)tan(alpha)=2/5alpha= 0.381R=sqrt(5^2+2^2)=sqrt(29)So, 5cos(theta) – 2sin(...

JW
Answered by Joe W. Maths tutor
10980 Views

The equation of the line L1 is y = 3x – 2 The equation of the line L2 is 3y – 9x + 5 = 0 Show that these two lines are parallel.

L1 is in the form y=mx+c where m is the gradient, 3.L2 can be rewritten as 3y=9x-5, then y=3x-(5/3) to reach y=mx+c. So, the gradient of L2 is 3.Therefore, both lines are parallel.

JW
Answered by Joe W. Maths tutor
4435 Views

The angles of a triangle are a, 2a and 2a + 30. Work out the value of a.

The areas of a triangle add up to 180 degrees. Therefore to tackle this question you must use algebra as you know that the sum of a, 2a and 2a + 30 is 180. a + 2a + 2a + 30 = 180 All the like terms can be...

AG
Answered by Amy G. Maths tutor
3576 Views

What does antithesis mean?

Antithesis is a literary device, quite similar to juxtaposition. But more explicitly, antithesis is the use of two opposites used in the same sentence to emphasise the contrasting effect. For example, 'Yo...

NP
Answered by Nina P. English tutor
3750 Views

How would I tackle questions regarding the depiction of education in Alan Bennet's play The History Boys?

Remember to always structure your essay as Point Evidence Explain.For example:(Point:)In The History Boys, the playwright Alan Bennet uses the characters of Hector, Irwin and the Headmaster to portray jux...

NP
3441 Views

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