Thread: Need help with trig graph questions

Hi, there are a few trig questions I'm not sure how to work out:

The equation y = a cos bx can be used to describe some natural cycles, such as tides and the phases of the moon.

1] Determine the constants a and b and write the equation representing the scenario.

a) A 12 hour gap between high tides of 2.3m and low tides of -2.3m
b) Same as a), except tides vary from 0.7m to 5.3m.

2] State the greatest possible value of 2sin(x - 30 deg) and the smallest possible value of x that will get this maximum value.

3] State the period, amplitude and range of this equation: y = -2sin(x - 45 deg) + 2

Thanks in advance for help, and please explain your working. Thanks!

Hello BG5965

Originally Posted by BG5965

Hi, there are a few trig questions I'm not sure how to work out:

The equation y = a cos bx can be used to describe some natural cycles, such as tides and the phases of the moon.

1] Determine the constants a and b and write the equation representing the scenario.

a) A 12 hour gap between high tides of 2.3m and low tides of -2.3m
b) Same as a), except tides vary from 0.7m to 5.3m.

2] State the greatest possible value of 2sin(x - 30 deg) and the smallest possible value of x that will get this maximum value.

3] State the period, amplitude and range of this equation: y = -2sin(x - 45 deg) + 2

Thanks in advance for help, and please explain your working. Thanks!

What you need to know about the graph of the equation :

Amplitude: varies between and . The value of is called the amplitude of the graph.

Period: the distance between corresponding points on consecutive cycles - for instance two consecutive peak values - is called the period. If is measured in degrees, the period is .

Initial value. When . So the graph starts at its maximum value.

1 a) The 12-hour gap between consecutive high tides gives the value of the period. So using the formula for the period above:

?

The maximum and minimum values are and , so the value of is ... ?

b) Here the values vary between and , a difference of . You'll notice that these values are exactly more than the values in (a). So

• the amplitude is still , but

• you'll need to add a constant value of to the equation in (a). Answer: (with the same values of and as before)

2) The sine function again takes values between and , with its first maximum occurring at . So varies between and , with the first maximum occurring when ?

3) Use the same ideas again to get the answers here.

Can you fill in the gaps?

Grandad