Solving trigonometric functions HSC question (1 Viewer)

BlueGas · May 30, 2015

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 · May 30, 2015

Help.

InteGrand · May 30, 2015

BlueGas said:
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!

$The general solution is $x=\tan^{-1} 2 + n\pi$, for $n\in \mathbb{Z}$. Or in approximate terms, $x\approx 1.107 + n\pi$.$

BlueGas · May 30, 2015

InteGrand said:
$The general solution is $x=\tan^{-1} 2 + n\pi$, for $n\in \mathbb{Z}$. Or in approximate terms, $x\approx 1.107 + n\pi$.$

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

BlueGas · Jun 10, 2015

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 · Jun 10, 2015

BlueGas said:
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 · Jun 10, 2015

InteGrand said:
That's mathematically correct too.

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

BlueGas · Jun 11, 2015

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 · Jun 11, 2015

This is just asking to graph something of the form $y=a\sin (b(x+c))$ , 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 $\frac{2\pi}{|b|}$ .

In our case, it's $y=\sin \left(2\left(x+\frac{\pi}{6}\right) \right)$ . 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 $\frac{\pi}{6}$ units to the left compared to y = sin x. The period is $\pi$ .

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

BlueGas · Jun 11, 2015

InteGrand said:
This is just asking to graph something of the form $y=a\sin (b(x+c))$ , 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 $\frac{2\pi}{|b|}$ .

In our case, it's $y=\sin \left(2\left(x+\frac{\pi}{6}\right) \right)$ . 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 $\frac{\pi}{6}$ units to the left compared to y = sin x. The period is $\pi$ .

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?

Solving trigonometric functions HSC question (1 Viewer)

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