Question

5. Given:
csc θ = −(17/15), where 270° ≤ θ ≤ 360° and
cot β = −(3/4) where 90° ≤ β ≤ 180°.

Answer 1

the angle is in the 3rd quadrant... and csc = 1/cos

find theta, then find

\[\theta = \arccos \frac{15}{17}\]

then theta is in the 3rd quadrant so its 180 plus the angle you found above.

same for the next question

2nd quadrant

cot = 1/tan

find

\[\beta = \arctan \frac{4}{3} \]

next subtract the angle found above from 180 to find beta.

Answer 2

I think there are some mistakes there...
For the first given condition.
First, csc θ = 1/sinθ.
Second, 270° ≤ θ ≤ 360° is quadrant IV. So, θ should be an angle in quadrant IV.

Actually, the question is incomplete. @jufrando has just posted the given conditions in the question but hasn't posted the whole (or exact) question - what we should solve for the question.

Answer 3

sorry this is what i got:

Evaluate the following, give exact value when possible:

sec(225°)
sin(-15°)
sin(75°)
Given:
csc θ = −(17/15), where 270° ≤ θ ≤ 360° and
cot β = −(3/4) where 90° ≤ β ≤ 180°.

Find the exact value of sin(θ + β). Show all the work.

Answer 4

or thats what it ask me to do

Answer 5

aah now that is a question
\[\sin(\theta+\beta)=\sin(\theta)\cos(\beta)+\sin(\beta)\cos(\theta)\] so you need the following numbers: \(\sin(\theta);\cos(\beta);\sin(\beta);\cos(\theta)\)

Answer 6

csc θ = −(17/15)
sin θ = 1/ [−(17/15)] = -15/17
So, adjacent sides \(=\sqrt{17^2 - 15^2} = \sqrt{64} = 8\)
cos θ = 8/15 (since it is in quadrant IV, it is positive.)

Answer 7

\[\csc(\theta)=-\frac{17}{15}\implies \sin(\theta)=-\frac{15}{17}\] so we got one

Answer 8

cot β = −(3/4)
tan β = 1/tanβ = 1/ [-(3/4)] = -4/3
So, opposite side = 4
adjacent side = 3
hypotenuse = \(\sqrt{4^2 + 3^3} = \sqrt{25} = 5\)
sin β = 4/5 (positive since it is in quad. II)
cos β = -3/5 (negative since it is in quad. II)

Answer 9

Special thanks to @satellite73 who gave you the formula you need. Now, plug in the values and get your answer :)

Answer 10

Oh ok thank you very much for both of you guys :), now i get it :D

Answer 11

Welcome :)