Choose the three true statements from the following.

Options
A) The period of y =cosx is 90◦.
B )The period of y =sinx is ð radians.
C) The period of y =sin(2x) is four times the period of y =sinx.
D) The period of y =sin(2x) is half of the period of y =sinx.
E) The graph of y =sinx only cuts the x-axis only once.
F) The graph of y =cosx cuts the y-axis at y = −1.
G) sin(30◦) = sin(150◦)
H) cos(30◦)=cos(−30◦)

To determine which statements are true, let's analyze each option one by one:

A) The period of y = cos(x) is 90°:
This statement is false. The period of y = cos(x) is actually 360° or 2π radians. The function cosine repeats itself every 360° or 2π radians, completing one full cycle.

B) The period of y = sin(x) is π radians:
This statement is true. The period of y = sin(x) is π radians or 180°. The function sine repeats itself every π radians or 180°, completing one full cycle.

C) The period of y = sin(2x) is four times the period of y = sin(x):
This statement is false. The period of y = sin(2x) is actually half the period of y = sin(x). When the input of sine function is multiplied by a constant, the period is compressed or expanded accordingly. Therefore, the period of y = sin(2x) is π/2 radians or 90°.

D) The period of y = sin(2x) is half of the period of y = sin(x):
This statement is true. As mentioned earlier, when the input of the sine function is multiplied by a constant, the period is compressed or expanded. When the input of y = sin(x) is multiplied by 2, the period is compressed to half. Therefore, the period of y = sin(2x) is π radians or 180°, half of the period of y = sin(x).

E) The graph of y = sin(x) only cuts the x-axis once:
This statement is false. The graph of y = sin(x) crosses the x-axis infinitely since sin(x) = 0 at multiple values of x, such as 0, π, 2π, etc. It oscillates above and below the x-axis as it completes each cycle.

F) The graph of y = cos(x) cuts the y-axis at y = -1:
This statement is true. The graph of y = cos(x) intersects the y-axis at y = -1 when x = (2n + 1)π/2 for all integers n. These are the points where the cosine function reaches its minimum value of -1.

G) sin(30°) = sin(150°):
This statement is true. The values of sine for 30° and 150° are equal. Since the sine function is symmetric about the y-axis, sin(30°) = sin(180° - 30°) = sin(150°).

H) cos(30°) = cos(-30°):
This statement is true. The cosine function is an even function, which means cos(-θ) = cos(θ) for any value of θ. Therefore, cos(30°) = cos(-30°).

From the given options, the three true statements are:
- B) The period of y = sin(x) is π radians.
- D) The period of y = sin(2x) is half of the period of y = sin(x).
- F) The graph of y = cos(x) cuts the y-axis at y = -1.