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In school, we just started learning about trigonometry, and I was wondering: is there a way to find the sine, cosine, tangent, cosecant, secant, and cotangent of a single angle without using a calc...
Edit: So really, if you press the sin, cos, or tan button and type in your number of degrees (°), the calculator will determine its approximate power of numbers. {Example above}: sin(x)≈x−x36+x5120−x75040
I should mention that for those first 4 problems, I think the point is actually not to use a calculator. The second part says ¨Find the function values. Round to four decimals places.¨: Cos 111.4° degree mode because there is a degree symbol. Sin(-18°) degree mode because there is a degree symbol
As Julien rightly noted. It uses power series of $\sin x, \cos x$ etc, to only approximately calculate the value of angles(in radians) you put in. You can read more about it here. And power series of $\tan x, \sec x$ and $\text{cosec } x$ is given here.
yes, sine=opp/hyp, cos=adj/hyp and tan=opp/adj. sin=3/√15 rationalized to be √15/5 cos=2/√15 rationalized to be 2√15/15 and tan =3/2 or 1.5 I guess am confused by the little curvy arrow in the picture that refers to angle a. I thought i had to find the angle?
Tables of sines came later in India, then in the Islamic world, then in Europe. Tangent tables started in the Islamic world. As far as I know there have been no cosine tables, for the good reason that $\cos A=\sin(90^\circ -A)$. And measuring was not used, too imprecise. $\endgroup$ –
You can look up cos and sin on the unit circle. The angles labelled above are those of the special right triangles 30-60-90 and 45-45-90. Note that -315 ≡ 45 (mod 360). For tan, use the identity $\tan{\theta} = \frac{\sin{\theta}}{\cos \theta}$.
$\begingroup$ With all of these, you probably want to reduce the number of polynomial terms you calculate; if you can get your angle values to within $\pi/4 \le \theta \le \pi/4$ (using complements and other angle-equivalence work) you can use fewer terms and still remain relatively accurate.
Did you mean 35 35 degrees or 35 35 radians? Do your calculators know that? 35 35 radians is 2005 2005 degrees. You may be trying to calculate degrees but the second calculator is calculator is calculator radians. cos350 = 0.8195204 cos 35 0 = 0.8195204 but cos 35 radians = −0.90369255 cos 35 r a d i a n s = − 0.90369255. That's what's ...
A calculator is broken so that the only keys that still work are the $\sin$, $\cos$, $\tan$, $\cot$, $\sin^{-1}$, $\cos^{-1}$, and $\tan^{-1}$ buttons. The display initially shows 0. (Assume that the calculator does real number calculations with infinite precision. All functions are in terms of radians.)