Question 1159219: Express as a trigonometric function of one angle.
cos 8 sin(−1) − cos 1 sin 8
Not sure how to write this. My professor only gave me double and half angle formulas so I am confused. Please help!
Answer by ikleyn(52879)   (Show Source):
You can put this solution on YOUR website! .
To solve the problem, you MUST know this formula, called "the sum of arguments for sine"
sin(a+b) = sin(a)*cos(b) + cos(a)*sin(b)
By applying this formula, you get
cos(8)*sin(-1) - cos(1)*sin(8) = -cos(8)*sin(1) - sin(8)*cos(1) = -(cos(8)*sin(1) + sin(8)*cos(1)) = -sin(9),
and it is your answer.
On the way, I used sin(-1) = -sin(1).
Note that the numbers in this post (in my and in yours) are measures of angles, expressed in degrees.
Solved.
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Regarding these basic trigonometry formulas, see the lessons
- FORMULAS FOR TRIGONOMETRIC FUNCTIONS
- Addition and subtraction formulas
- Addition and subtraction formulas - Examples
in this site.
They are REALLY BASIC: everybody studying Trigonometry MUST know them as the multiplication table.
At least, he (or she) must know that they do exist, and also must know, where to find them . . .
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