Question

Pre-calc questions (trignometry)

Answer 1

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)

$\sin\theta=\dfrac{y}{r}=\dfrac{-\sqrt{39}}{8}$              $\csc\theta=\dfrac{r}{y}=\dfrac{-8}{\sqrt{39}}$  rationalized = $\dfrac{-8\sqrt{39}}{39}$

$\cos\theta=\dfrac{x}{r}=\dfrac{-5}{8}$                  $\sec\theta=\dfrac{r}{x}=\dfrac{-8}{5}$  (GIVEN)

$\tan\theta=\dfrac{y}{x}=\dfrac{\sqrt{39}}{5}$              $\cot\theta=\dfrac{x}{y}=\dfrac{-5}{-\sqrt{39}}$  rationalized = $=\dfrac{5\sqrt{39}}{39}$

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