Question

what is the maximum and minimum values of sin theta.

Answer 1

Step-by-step explanation:

Properties Of The Sine Graph

Maximum value of sin θ is 1 when θ = 90 ˚. Minium value of sin θ is –1 when θ = 270 ˚. So, the range of values of sin θ is –1 ≤ sin θ ≤ 1.

Answer 2

Therefore, the maximum and minimum values of sinθ are 1 and -1 respectively.

Given

sinθ

To Find

The maximum and minimum values of sinθ

Solution

Here we need to maximize and minimize sinθ

Let Z = sinθ

differentiating Z with respect to θ we get

Z' or dZ/dθ = cosθ

Now assuming Z' = 0 we get,

cosθ = 0

or, θ = π/2 or, 3π/2

Differentiating Z' with respect to θ we get,

Z" or d²Z/dθ² = -sinθ

Now we will put π/2 or, 3 π/2 in the value of Z".

• If Z" is negative, it is the maximum value of Z.
• If it is positive, it is the minimum value for Z

Z"(π/2) = -sinπ/2 = -1

Hence we get the maximum value for sinθ for θ =π/2

Z"(3π/2) = -sin(3π/2) = -(-1)

= 1

Hence we get the minimum value for sinθ for θ = 3π/2

Therefore, maximum value for sinθ = sinπ/2 = 1

minimum value for sinθ = sin3π/2 = -1

Therefore, the maximum and minimum values of sinθ are 1 and -1 respectively.

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