Yahoo Answers is shutting down on May 4th, 2021 (Eastern Time) and beginning April 20th, 2021 (Eastern Time) the Yahoo Answers website will be in read-only mode. There will be no changes to other Yahoo properties or services, or your Yahoo account. You can find more information about the Yahoo Answers shutdown and how to download your data on this help page.
Trending News
Trigonometry Question?
Suppose csc(90-θ)=3/2. without using inverse trig functions, find the value of sin θ, sec θ, and cot θ
3 Answers
- ?Lv 73 months ago
csc(90 - θ) = 3/2. sin θ,
sin(θ) = sin(90 - sin^(-1)(2/3)), sin(θ) = -sin(90 + sin^(-1)(2/3))
sec(θ) = sec(90 - sin^(-1)(2/3)), sec(θ) = -sec(90 + sin^(-1)(2/3))
and
cot(θ) = cot(90 - sin^(-1)(2/3)), cot(θ) = cot(90 + sin^(-1)(2/3)
- az_lenderLv 73 months ago
sec(theta) = 3/2, cos(theta) = 2/3, sin(theta) = sqrt(1 - 4/9) = sqrt(5)/3,
cot(theta) = cos(theta)/sin(theta) = 2/sqrt(5).
If theta happens to be in the 4th quadrant, the sine and cotangent will be negative.
If theta's in the first quadrant, all of the above functions are positive.
The fact that csc(90 - theta) > 0 shows that theta cannot be in the 2nd or 3rd quadrant.
