Question

In: Math

If csc x = 2 and x is in Q I, determine the exact values of...

If csc x = 2 and x is in Q I, determine the exact values of sin x and cos x.

Solutions

Expert Solution

Some trigonometric relations required to solve the problem:

-----------------------------------------------------------------------------------------------------------------

It is given that and x is in the first quadrant.

In the first quadrant, are also positive.

we know that,  

                           

                              

--------------------------------------------------------------------------------------------------------------------------

Now we know that

so   

---------------------------------------------------------------------------------------------------------------------------------------


Related Solutions

Determine whether the given differential equation is exact. If it is exact, solve it. i) (x...
Determine whether the given differential equation is exact. If it is exact, solve it. i) (x 3 + y 3 )dx + 3xy2 dy = 0, Ans. x 4 + 4y 3x = C ii) (y ln y − e −xy) + (1 y + x ln y) dy dx = 0, Ans. not exact iii) (e −x sin y − 3)dx − (3x 2 − e x sin(2y))dy = 0, Ans. not exact iv) (xy − 1)dx + (x...
Given that Csc(x) = - 3 and Cos(x) < 0, find the exact value of each...
Given that Csc(x) = - 3 and Cos(x) < 0, find the exact value of each of the trigonometric function of x. Functions are: a. Sin(x) , b. Cos(x) , c. Tan(x) , d. Csc(x) , e. Sec(x) , f. Cot(x)
y'=tan(x)^2(csc(y)^3)
y'=tan(x)^2(csc(y)^3)
Determine if exact equation, then solve: x(y+2)y' = lnx+1 , y(1) = -1
Determine if exact equation, then solve: x(y+2)y' = lnx+1 , y(1) = -1
Differentiate. 1a) p(x) = 4th root of (2x-3/x^3) b) q(x)= (2 sinx)/(1-cosx) c)r(x)= sin(csc^3(x^4)) d) U(x)=...
Differentiate. 1a) p(x) = 4th root of (2x-3/x^3) b) q(x)= (2 sinx)/(1-cosx) c)r(x)= sin(csc^3(x^4)) d) U(x)= ((cube root of x^2) sinx -2x-3)/sq. rt. x
1. Determine the absolute minimum and maximum values of the function f(x) = x^3 - 6x^2...
1. Determine the absolute minimum and maximum values of the function f(x) = x^3 - 6x^2 + 9x + 1 in the following intervals: a) [0,5] b) [-1,2] 2. A company produces and sells x number of calculators per week. The functions for demand and cost are the following: p = 500 - 0.5x and c(x) = 10,000 + 135x. Determine: a) Function of weekly revenue b) Price and number of calculators that have to be sold to maximize revenue...
Determine whether the equation is exact. If it is exact, find the solution. If it is...
Determine whether the equation is exact. If it is exact, find the solution. If it is not, enter NS. (8x^2−2xy+5)dx+(8y^2−x^2+8)dy=0
Consider the function q(x)=x^11−3x^10+2. Find the x-coordinates of all local maxima. If there are multiple values,...
Consider the function q(x)=x^11−3x^10+2. Find the x-coordinates of all local maxima. If there are multiple values, give them separated by commas. If there are no local maxima, enter ∅.
Utilize identities to calculate the exact value of the five remaining trigonometric functions if: csc(α)= √3,...
Utilize identities to calculate the exact value of the five remaining trigonometric functions if: csc(α)= √3, π/2, < α < π Calculate the equivalent algebraic expression for: sec(arcsin(x - 1)
a) Determine whether the given differential equation is exact. If it is exact, solve it. (If...
a) Determine whether the given differential equation is exact. If it is exact, solve it. (If it is not exact, enter NOT.) (2xy2 − 5) dx + (2x2y + 4) dy = 0 b) Solve the given differential equation by finding, as in Example 4 of Section 2.4, an appropriate integrating factor. (6 − 20y + e−5x) dx − 4 dy = 0
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT