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UPSC CDS 2 2020 Math Paper

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Question : 54 of 100

Marks: +1, -0

What is the maximum value of 3 sin θ - 4?

$-4$
$-1$
0
1

Solution:

Concept:

The maximum value of

3 \sin \theta - 4

occurs when

\sin \theta

is maximum. The maximum value of

\sin \theta

is

1

.

Explanation:

Substitute

\sin \theta = 1

into the expression:

3 \sin \theta - 4 = 3(1) - 4

= 3 - 4

= -1

No other value of

\sin \theta

gives a larger result because

\sin \theta \le 1

.

Answer:

The maximum value is

-1

, which corresponds to option B.

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