Answer: (1a) 250° (1b) 70° (2) see below
Step-by-step explanation:
1a) -110 + 360 (one rotation clockwise) = 250°
1b) 430 - 360 (one rotation counterclockwise) = 70°
2) sec Ф = -8/5 in Quadrant III
Quadrant III identifies that both sin (y) and cos (x) are negative.
sec = r/x --> r = 8, x = -5, and y = -√39
(Use Pythagorean Theorem x² + y² = r² to solve for y)
[tex]\sin\theta=\dfrac{y}{r}=\dfrac{-\sqrt{39}}{8}[/tex] [tex]\csc\theta=\dfrac{r}{y}=\dfrac{-8}{\sqrt{39}}[/tex] rationalized = [tex]\dfrac{-8\sqrt{39}}{39}[/tex]
[tex]\cos\theta=\dfrac{x}{r}=\dfrac{-5}{8}[/tex] [tex]\sec\theta=\dfrac{r}{x}=\dfrac{-8}{5}[/tex] (GIVEN)
[tex]\tan\theta=\dfrac{y}{x}=\dfrac{\sqrt{39}}{5}[/tex] [tex]\cot\theta=\dfrac{x}{y}=\dfrac{-5}{-\sqrt{39}}[/tex] rationalized = [tex]=\dfrac{5\sqrt{39}}{39}[/tex]
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