Trigonometry Answers

A ladder AB which is setup with B on the horizontal ground and A against a vertical wall, makes an angle of 71 degrees with the ground. it is prevented from slipping by a tight rope PQ of length 1.68 metres, fixed at P to the foot of the wall and at Q to the ladder, PQ being at right angles to AB. Calculate in centimetres
a) The height AP of the ladder above P
b) The length of the ladder?

4. (a) Suppose a particle P is moving in the plane so that its coordinates are given by P(x,y), where x = 4cos2t, y = 7sin2t.
(i) By finding a, b ∈ R such that x^2/a^2+y^2/ b^2 = 1, show that P is travelling on an elliptical
path.
(ii) Let L(t) be the distance from P to the origin. Obtain an expression for L(t).
(iii) How fast is the distance between P and the origin changing when t = π/8?

prove that
(2cosθ−1)(2cosθ−1)(2cos2θ−1)=2cos4θ+1

Express   Sin Cos y 8 6   in the form       rSin y , where  is an acute angle in
degrees.

If n is a positive integer, prove that (√3+1)^n +(√3-1)^n = 2^n+1 cosπn/6

Prove that (1+costheta+isintheta)^n + (1+costheta-isintheta)^n =2^n+1 cos^n π/2 cosntheta/2

Simplify (cos2π/3 + isin2π/3)^1/4 and express the result in a form free from trigonometrically expression.

Expand cos6theta and sin6theta in terms of costheta and sintheta