In which quadrant does θ lie if the following statements are true:cosecant, theta, is less than, 0, and , cotangent, theta, is less than, 0cscθ<0 and cotθ<0
Question
In which quadrant does θ lie if the following statements are true:
- cosecant **
- cotangent **
Solution
The given conditions are cscθ < 0 and cotθ < 0.
-
The cosecant function, cscθ, is negative in the third and fourth quadrants of the unit circle. This is because cosecant is the reciprocal of sine, and sine is negative in these quadrants.
-
The cotangent function, cotθ, is negative in the second and fourth quadrants. This is because cotangent is the reciprocal of tangent, and tangent is negative in these quadrants.
Therefore, given that both conditions must be true, θ must lie in the fourth quadrant where both cscθ and cotθ are negative.
Similar Questions
In which quadrant does θ lie if the following statements are true:secant, theta, is greater than, 0, and , cosecant, theta, is less than, 0secθ>0 and cscθ<0
Assertion : The value of sin 𝜃 = &' is not possible.Reason : Hypotenuse is the largest side in any right angled triangle.
–𝜋2≤θ≤𝜋2. Find the value of θ in radians.sin(θ)=–12Write your answer in simplified, rationalized form. Do not round.θ=
Which of the following expressions is not equivalent to cot2θ?csc 2θ + 1( ) 2csc 2θ - 1
When converting a complex number from rectangular form to polar form, "θ" must always be expressed in radians.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.