SOLUTION: Using the basic identities, find the value of cscΘ if cotΘ = -12/5.
Algebra.Com
Question 1093671: Using the basic identities, find the value of cscΘ if cotΘ = -12/5.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the triangle formed is a right triangle in the second quadrant.
the hypotenuse of that triangle is equal to the square root of the sum of the legs squared which is equal to sqrt(12^2 + 5^2) = sqrt(169) = 13.
see the diagram below:
in this triangle:
opposite side of the angle is equal to 5.
adjacent side of the angle is equal to -12.
hypotenuse of the triangle formed is equal to 13.
i called the angle T which stands for theta in this case.
sin(T) = opposite / hypotenuse = 5/13.
csc(T) = hypotenuse / opposite = 13/5
csc(T) is also equal to 1 / sin(t) = 1 / (5/13) = 13/5.
that's your answer.
csc(T) = 13/5
general formula used to find the hypotenuse:
c^2 = a^2 + b^2
c is the hypotenuse
a is one of the legs of the right triangle.
b is the other leg of the right triangle.
length of the hypotenuse is found by finding sqrt(c^2).
when graphing the angle and the right triangle formed:
x = a
y = b
h = c
formula becomes h^2 = x^2 + y^2
x is the side adjacent to the angle formed.
y is the side opposite to the angle formed.
h is the hypotenuse of the right triangle formed.
the angle formed is at the origin of the graph which is the intersection of the x and y axes.
RELATED QUESTIONS
From using trigonometric identity sinē Θ + cosē Θ = {{{ 1 }}}, obtain the... (answered by Alan3354,rothauserc)
If tan theta=cot<60`+theta> find the value of theta
tanΘ = cot(60 + Θ) ,... (answered by sanusi hammed )
find the exact value for sin(Θ/2) given sin Θ=12/13; Θ is obtuse.
(answered by solver91311)
If sin Θ = 2/3 and tan Θ < 0, what is the value of cos... (answered by stanbon)
Suppose Θ is an angle in standard position whose terminal side lies in quadrant IV... (answered by amarjeeth123)
Suppose Θ is an angle in standard position whose terminal side lies in quadrant IV... (answered by lwsshak3)
Hi,
I'm very lost. The direction said to find the exact value of Θ in the interval (answered by stanbon)
If sin Θ = 5 over 6, what are the values of cos Θ and tan Θ
(answered by lwsshak3)
If sin Θ = 5/6 , what are the values of cos Θ and tan... (answered by Maruf)