I'm new to trigonometric equations but want to teach myself.
How would I approach, for e.g. simple problems like:
(i)sin(x) = - 0.25
(ii)cos(3x+0.42)=0.23
thanks any help for the above would be greatly appreciated!
dan
I'm new to trigonometric equations but want to teach myself.
How would I approach, for e.g. simple problems like:
(i)sin(x) = - 0.25
(ii)cos(3x+0.42)=0.23
thanks any help for the above would be greatly appreciated!
dan
Hi Dan,
First, since you are new to trig equations I would suggest that you memorize the basic values of trig functions for the unit circle. For example, it is good to know off the top of your head that
$\displaystyle \sin(\frac{\pi}{6})=\frac{1}{2}$
When you know the value of the trig functions at the standard angles, you will easily be able to recall these when given an equation like the one above. Looking at
$\displaystyle \sin(x)=-0.25$
you will know that you will have to probably use a calculator to get an approximation of the answer. What this problem says in words is "The sine of x is equal to negative 25 hundredths". We can rearrange the equation to say this:
$\displaystyle \sin^{-1}(-.025)=x$
This reads in words as "The angle whose sine is 25 hundredths equals x".
There is no exact value from the standard angles whose sine is -0.25. There might be some equation you could use to find this, but if there is I'm having a massive brain block.
If the problem had read:
$\displaystyle \sin(x)=\frac{1}{2}$ then we could recall from our memorized trig values that the angles whose sine is 1/2 are $\displaystyle \frac{\pi}{6}$ and $\displaystyle \frac{5\pi}{6}$
Basically the key to being successful in trig is knowing the standard angles in multiples of $\displaystyle \frac{\pi}{6}$ from 0 to $\displaystyle 2\pi$ and their values for sine cosine. Also, knowing the basic identities is key.
-liz.
PS. I'm not guaranteeing the accuracy of this information because I have been studying for my calc II test for several hours and my brain is fried...if someone has a correction please comment on this post! Cheers!