DOMAIN OF COSEC SEC AND COTANGENT

Find the principal value of the following.

Problem 1 :

Solution :

For what angle measure of sec, we get 2/√3. The angle measure should lie in between [0, π].

𝜃 = π/6 ∈ [0, π]

So, the required angle measure is π/6.

Problem 2 :

Solution :

For what angle measure of cot, we get √3. The angle measure should lie in between (0, π).

tangent and cotangent they are reciprocal to each other. We know, tan π/6 = 1/√3, then cotangent π/6 = √3

𝜃 = π/6 ∈ (0, π)

So, the required angle measure is π/6.

Problem 3 :

Solution :

cosec (-𝜃) = -cosec 𝜃

cosec^-1 (-√2) = -cosec^-1(√2)

For what angle measure of cosec, we get √2. The angle measure should lie in between [-π/2, π/2].

cosec and sin they are reciprocal to each other. We know, sin π/4 = 1/√2, then cosec π/4 = √2

𝜃 = π/4 ∈ [-π/2, π/2]

= -cosec^-1(√2)

= -π/4

So, the required angle measure is -π/4.

Problem 4 :

Solution :

Problem 5 :

Solution :

Problem 6 :

Solution :