1.11: Solve related trigonometric equations

4PM1/2/June/2021 — Question 10 · 10 marks

(a) Solve the equation
tan x∘=−3for0≤x<360.\mathrm{tan}\,x^\circ=-3 \qquad \text{for} \qquad 0\leq x<360.
Give your solutions to the nearest whole number.
(3)
Given that
7sin2θ+sin θ cos θ=6,7\mathrm{sin}^2\theta+\mathrm{sin}\,\theta\,\mathrm{cos}\,\theta=6,
(b) show that
tan2θ+tan θ−6=0.\mathrm{tan}^2\theta+\mathrm{tan}\,\theta-6=0.
(3)
(c) Hence solve the equation
7sin2y∘+sin y∘ cos y∘=6for0≤y<360.7\mathrm{sin}^2y^\circ+\mathrm{sin}\,y^\circ\,\mathrm{cos}\,y^\circ=6 \qquad \text{for} \qquad 0\leq y<360.
Give your solutions to the nearest whole number.
(4)