A few days ago
need help evaluating these trigonometric equations.?
1) sin^-1(-1/2)
2) sin^2 (5pi/6)
3) cot(2pi/3)
4) cot^-1(-1)
5) sec (3pi/4)
Top 2 Answers
A few days ago
Favorite Answer
1)The angle whose sine is -1/2 is -30 degrees, or -Pi/6 radians. Therefore the arcsin (as you’ve written sin^-1 (-1/2)) is -Pi/6, or if you would prefer to keep the answer positive instead, 11*Pi/6 radians. The answer could also be in quadrant 3, at 7*Pi/ 6 radians.
2) Similarly, since sin(5*Pi/6) is 1/2, (sin(5Pi/6))^2= (1/2)^2 =1/4
3) cot(x) = 1/(tan(x)) = cos(x)/sin(x)
cos(2*Pi/3) = -1/2, sin(2*Pi/3) = sqrt(3)/2,
so cot(2*Pi/3) = (-1/2)/(sqrt(3)/2) = -1/sqrt(3)
4) see above for definition of cotangent. Then for cos(x)=sin(x), |x| = Pi/4, or 45 degrees.
Since this is negative, it can either be in quadrant 2 or quadrant 4. so the answer could be 3*Pi/4 or 7*Pi/4.
5)sec(x) = 1/cos(x). cos(3*Pi/4) = -1/sqrt(2)
so sec(3*Pi/4) = -sqrt(2)
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A few days ago
do you have your graphing calculator handy?…these are great calculator questions…
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