Trigonometry help
Taking online classes and trying to find the angle in degrees of csc when given a decimal
Example in text not helping
Question is csc (theta) = 1.245 and they want an angle in degrees
Thank you in advance Lisa
$\endgroup$ 22 Answers
$\begingroup$Almost all calculators are programmed with just the sine function ($\sin$), the cosine function ($\cos$), and the tangent function ($\tan$). To work with the secant, cosecant and cotangent functions, we need to use some trig identities and some algebra.
Your problem asks us to solve for $\theta$ where $\csc\theta=1.245$.
We know that $\csc\theta=\frac{1}{\sin\theta}$. Using this identity, we solve for $\theta$.
\begin{align} \csc\theta&=1.245\\ \frac{1}{\sin\theta}&=1.245\\ \frac{1}{1.245}&=\sin\theta\\ \sin^{-1}\frac{1}{1.245}&=\theta \end{align}
Remember that $\sin^{-1}$ is the inverse sine, also denoted as $\arcsin$. Using the calculator, we find that $\sin^{-1}(1/1.245)=53.44^{\circ}\text{ or }0.933\text{ radians}$.
$\endgroup$ 5 $\begingroup$All you need to do is take the inverse function to return the original angle. We know that $\csc (\theta)= 1.256$, so solving for $\theta$
$\csc^{-1}(\theta)=\csc^{-1}(1.245)=\ \approx53.44$ degrees
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