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 :
May 21, 24 08:51 PM
May 21, 24 08:51 AM
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