Solving trigonometric functions HSC question (1 Viewer)

[BlueGas]

Solve tanx=2, express your answer in radian measure correct to two decimal places.

I have no clue doing this question so please take it easy while explaining, I want to know the method to answering these type of questions so I can answer other questions similar to this, thanks!

 

[BlueGas]

Help.

 

[InteGrand]

Solve tanx=2, express your answer in radian measure correct to two decimal places.

I have no clue doing this question so please take it easy while explaining, I want to know the method to answering these type of questions so I can answer other questions similar to this, thanks!

 

[BlueGas]

Ah, you have to use tan inverse, thanks man.

 

[BlueGas]

Just a quick question, why is the answer wrong if you do (in degrees mode) tan inverse (2) = 63.43... and then you change it to radians, why is that wrong?

 

[InteGrand]

Just a quick question, why is the answer wrong if you do (in degrees mode) tan inverse (2) = 63.43... and then you change it to radians, why is that wrong?

That's mathematically correct too.

 

[BlueGas]

That's mathematically correct too.

Oh okay, because the solutions didn't mention it.

 

[BlueGas]

How would I go about solving this question? I know you have to graph but to come up with your graph you need to solve, and a simple inverse won't work, so what should I do? Please also take it easy while explaining, and please explain how you come up with your working out.

 

[InteGrand]

This is just asking to graph something of the form , which you should be able to do. The |a| tells us the amplitude, the b tells us about how compressed the graph is in the horizontal direction compared to a normal sine graph y = sin x, and the c tells us how much the graph is shifted horizontally compared to y = sin x. The period of the function is .

In our case, it's . So the amplitude is 1, the graph is compressed horizontally by a factor of 2 compared to y = sin x, and there is a horizontal shift of units to the left compared to y = sin x. The period is .

Also, when x = 0, y = sin(π/3) > 0, so the y-intercept is positive (so you can rule out option (A)).

 

[BlueGas]

This is just asking to graph something of the form , which you should be able to do. The |a| tells us the amplitude, the b tells us about how compressed the graph is in the horizontal direction compared to a normal sine graph y = sin x, and the c tells us how much the graph is shifted horizontally compared to y = sin x. The period of the function is .

In our case, it's . So the amplitude is 1, the graph is compressed horizontally by a factor of 2 compared to y = sin x, and there is a horizontal shift of units to the left compared to y = sin x. The period is .

Also, when x = 0, y = sin(π/3) > 0, so the y-intercept is positive (so you can rule out option (A)).

Is there another simpler way?