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Question

Let 0° < t < 90°. Which of the following is true about the relationship between sin(t) and cos(t)?

Accepted Answer

Let's analyze the relationship between sin(t) and cos(t) for 0° < t < 90°: - At t = 45°, sin(45°) = cos(45°) = 1/√2. - For t < 45°, sin(t) < cos(t). This is because as t increases from 0° to 45°, sin(t) increases from 0 to 1/√2, while cos(t) decreases from 1 to 1/√2, but cos(t) remains greater than sin(t) until t = 45°. - For t > 45°, sin(t) > cos(t). After 45°, sin(t) continues to increase while cos(t) continues to decrease. Therefore, the correct statement is: 'sin(t) < cos(t) when t < 45°.'

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