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A day full of math games & activities. Find one near you.
Find the value of each of the following:
(i) tan-1 (1/√3)
(ii) tan-1 (-1/√3)
(iii) tan-1 (cos (π /2) )
(iv) tan-1 (2 cos (2π /3) )
To find the values of the above inverse trigonometric ratios, we will use trigonometric identities.
Answer: The value of inverse tan ratios are (i) is π / 6, (ii) is - π / 6, (iii) is 0 and (iv) is - π / 4.
Let's find the values of inverse trigonometric ratios.
Explanation:
(i) Let tan-1 (1/√3) = θ
⇒ tan θ = 1/√3
⇒ tan θ = tan (π / 6)
⇒ θ = π / 6
(ii) Let tan-1 (-1/√3) = θ
⇒ tan θ = - 1/√3
⇒ tan θ = tan (- π / 6)
⇒ θ = - π / 6
(iii) Let tan-1 (cos (π/2)) = θ
⇒ tan θ = cos π/2
As we know that cos π/2 = 0
⇒ tan θ = 0
⇒ θ = 0
(iv) Let tan-1 (2 cos (2π /3) ) = θ
⇒ tan θ = 2 cos (2π /3)
⇒ tan θ = 2 cos (π - π /3)
As we know that cos π is 180º = -1 and cos π /3 is cos 60º = 1/ 2
⇒ tan θ = -2 cos (π/3)
⇒ tan θ = -2 × (1/2)
⇒ tan θ = - 1
⇒ tan θ = tan (- π / 4)
⇒ θ = - π / 4
Thus, the values of inverse tan ratios are (i) is π / 6, (ii) is -π / 6, (iii) is 0 and (iv) is - π / 4.
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