Question

Which statements correctly describe the cosine and sine functions? Check all that apply.

The cosine function increases on (90°, 180°) and (270°, 360°).

The sine function increases on (0°, 90°) and (270°, 360°).

The cosine function decreases on (0°, 180°).

Both the cosine and sine functions have a minimum value of 0.

Both the cosine and sine functions have a maximum value of 1.

Both the cosine and sine functions are periodic.

Answer 1

Answers:

B: The sine function increases on (0°, 90°) and (270°, 360°).

C: The cosine function decreases on (0°, 180°).

E: Both the cosine and sine functions have a maximum value of 1.

F: Both the cosine and sine functions are periodic.

Answer 2

The only statements that correctly describe the cosine and sine functions are;

Option B: The sine function increases on (0°, 90°) and (270°, 360°).

Option C: The cosine function decreases on (0°, 180°).

Option E: Both the cosine and sine functions have a maximum value of 1.

Option F: Both the cosine and sine functions are periodic.

To answer this question, we need to first write the sine and cosine of angles 0°, 90°, 180°, 270° and 360°.

sin 0° = cos  90° = 0

cos 0° = sin 90° = 1

sin 180° = cos 270° = 0

cos 180° = sin 270° = -1

cos 360 = 1

sin 360 = 0

Let us look at the options;

Option A; Statement is not correct because cosine decreases from 90° to 180°.

Option B; This statement is correct because sine increases from 0 to 1 on (0°, 90°) and increases from -1 to 0 on (270°, 360°).

Option C; This statement is true because cosine decreases from 1 to -1 on (0°, 180°).

Option D; This statement is not true because they can also have negative values which are lesser than 0.

Option E; This statement is true because they both have a maximum value of 1.

Option F; This is true because since they repeat values they are said to be periodic.

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