Solving Trig Equations Flashcards

All 4 cards in this deck

What are the steps to solve $\sin x^\circ = k$ for $0 \le x \le 360$?

e.g. $2\sin x^\circ = -1$

1. Rearrange: $\sin x^\circ = -0.5$
2. Find the related acute angle: $\sin^{-1}0.5 = 30$
3. Use the sine graph's symmetry (sine negative after $180^\circ$): $x = 210$ and $x = 330$.

If $x$ is a solution of $\cos x^\circ = k$, how do you find the other solution in $0 \le x \le 360$?

Use $360 - x$.
e.g. if $x = 60$ then the other solution is $300$.

If $x$ is a solution of $\tan x^\circ = k$, how do you find further solutions?

Add or subtract $180$ each time, since the tangent graph has period $180^\circ$.

True or false? $\sin x^\circ = 0.6$ has exactly one solution for $0 \le x \le 360$.

False.
It has two, symmetric about $x = 90$ (e.g. about $37$ and $143$).