Question

P(3,-3) lies on the terminal arm of an angle in standard position.

a. Draw a sketch of the principal angle (θ) in standard position. Label θ AND the related acute

angle, RA. [2 marks]

b. Determine the exact primary trig ratios for θ. Show ALL your work. You do not need to

rationalize the denominator, but you must simplify your radical and your ratios. [5 marks]

c. Determine the values of the principal angle and related acute angle to the nearest degree.

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

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