Question

Let sin t = a, cos t = b, and tan t = c. Write the following expression in terms of a, b, and c.

sin (t + 4pi) - cos (t + 8pi) + tan (t + 5pi)

Answer 1

\[(\sin(t)\cos(4 \pi)+\sin(4 \pi)\cos(t))-(\cos(t)\cos(8 \pi)-\sin(t) \sin(8\pi))\]
\[+\frac{\tan(t)+\tan(5 \pi)}{1-\tan(t) \tan(5 \pi)}\]

Answer 2

\[(\sin(t) (1)+(0)\cos(t))-(\cos(t)(1)-\sin(t)(0))+\frac{\tan(t)+0}{1-\tan(t)(0)}\]

Answer 3

\[\sin(t)+0-\cos(t)+0+\frac{\tan(t)}{1-0}=\sin(t)-\cos(t)+\tan(t)\]

Answer 4

\[=a-b+c\]

Answer 5

http://www.sosmath.com/trig/prodform/prodform.html

see if you can use these formulas to manipulate your equation

Answer 6

Trigonometric formulas. Yes, I should have done that...thanks to you both.

Answer 7

*identities