Answer to Question #285981 in Trigonometry for vicky

Question #285981

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.


1
Expert's answer
2022-01-10T16:37:49-0500

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"



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