Example A-7.1

Use Maple to find the identities for $\sin \left(x\+y\right)$ and $\cos \left(x-y\right)$ and check the results.

Example A-7.2

Two sides of a triangle have lengths a = 5 and b = 2 and the angle between them is $C\=52°$. Use the Law of Sines and the Law of Cosines to find the other side c and the other two angles A and B opposite a and b, respectively.

Example A-7.3

For the equation $6 {\cos }^2\left(x\right)-\cos \left(x\right)-2\=0$, find all solutions in the interval $\left[0\,2 \mathrm{\π}\right]\.$

Example A-7.4

For the equation $2 {\sin }^2\left(x\right)\+3 \cos \left(x\right)\=3$, find all solutions in the interval $\left[0\,2 \mathrm{\π}\right]$.

Example A-7.5

For the equation $4 \sin \left(x\right)\+7 \cos \left(x\right)\=8$, find all solutions in the interval $\left[0\,2 \mathrm{\π}\right]\.$

Example A-7.6

Express $\cos \left(4x\right)+4\cos \left(2x\right)+3$ in terms of $\cos \left(x\right)$.

Example A-7.7

What is the domain for the principal branch of $\sin \left(x\right)$?

Example A-7.8

If $f\left(x\right)$ is any one of the six elementary trig functions, examine the role of the parameters $a\,b\,h\,k$ in the transformation $a f\left(b\left(x-h\right)\right)\+k$.

Example A-7.9

Obtain a Maple graph of the sine function where the argument is given in degrees, not radians.