Answer to Question #178968 in Trigonometry for Raine

Question

Angle θ is the principle angle in standard position with its terminal arm in the Quadrant III, such that O° ≤ θ ≤ 360°. Given that cos θ = -2/7

a) Sketch angle θ in standard position

b) Determine the exact values of the other two primary trig ratios in the simplest form

c) Determine the value of the principal angle to the nearest degree. Show your work.

Answer 1

a)

b) $y=\sqrt{r^2-x^2}=\sqrt{7^2-2^2}=\sqrt{49-4}=\sqrt{45}=3\sqrt{5}$

$sin \theta=-\frac{y}{r}=-\frac{3 \sqrt{5}}{7}$

$tan \theta=\frac{y}{x}=\frac{3 \sqrt{5}}{2}$

c) $tan \theta=\frac{y}{x}=\frac{3 \sqrt{5}}{2} \implies \theta= tan^{-1}\frac{3 \sqrt{5}}{2}=73.4$

$\theta_{Total}=180+73.4=253.4 =253^0$