Recently I have been covering trig identities in maths. One part of this is for example is being able to calculate another angle whose sine is is $0.990$, given that $\sin 98^\circ = 0.990$. Obviously this can be done by sketching a graph but is there any quick way of doing this on a graphical calculator?
2025-01-13 02:08:27.1736734107
How to find values of trigonometric functions, using identities and a calculator?
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As @kamil09875 pointed out, you got the equation wrong: you meant $\sin 98°=0.990$.
The sine of $98°$ is not exactly $0.990$ but it is close: it is more like $0.990268068742$.
If your question really is to find another angle whose sine is $0.990$, any scientific calculator (which includes graphing calculators) can do this if you type
$$\sin^{-1}(0.990)$$
If your calculator is in degree mode, it will give you the answer
or something close to it. If your calculator is not in degree mode but rather in radian mode, there are several ways to convert the answer to degrees, such as multiplying the radian answer by $\frac{180°}{\pi}$. Some calculators have another way: my TI-Nspire CX has a command $\blacktriangleright \mathrm{DD}$ that does the conversion.
The function $\sin^{-1}$ will return a value between $-90°$ and $90°$. It will not return other values that give the same sine. In your case, you had a value outside that range, so the calculator did indeed return a different value.
Note that if your problem was just to find another angle whose sine is the same as that of $98°$, the easiest way is to subtract that angle from $180°$, giving
which is close to the angle I gave you but is not exactly the same. This works because of the trigonometric identity
$$\sin(180°-x)=\sin(x)$$
or, in radians,
$$\sin(\pi-x)=\sin(x)$$