Question

Pre-calc questions (trignometry)

Answer 1

Answer: (1a) 250° (1b) 70° (2) see below

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=(y)/(r)=(-√(39))/(8)`
`\csc\theta=(r)/(y)=(-8)/(√(39))` rationalized =
`(-8√(39))/(39)`

`\cos\theta=(x)/(r)=(-5)/(8)`
`\sec\theta=(r)/(x)=(-8)/(5)` (GIVEN)

`\tan\theta=(y)/(x)=(√(39))/(5)`
`\cot\theta=(x)/(y)=(-5)/(-√(39))` rationalized =
`=(5√(39))/(39)`

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