In right triangle ABC, C is the right angle and sin A = sqrt3/2. what is the value of cscB?

Question

anonymous · Answer

hmm....... Cosines.....
 so here we go! can i get a figure

anonymous · Answer

$$a^2 + b^2 = c^2$$
 take this prime formula!

anonymous · Answer

$$a^2\over c^2 $$+$$ b^2\over c^2 $$
But a2/c2 = (sin A)2, and b2/c2 = (cos A)2. In order to reduce the number of parentheses that have to be written, it is a convention that the notation sin2 A is an abbreviation for (sin A)2, and similarly for powers of the other trig functions. Thus, we have proven that
$$\sin^2 A + \cos^2 A = 1$$

anonymous · Answer

This problem can be ground out and solved, but I think the real issue here is being able to recognize the special values of sin x that come from a 30-60-90 triangle.  sin A = sqrt3/2 indicates a sixty degree angle at A; in turn, this indicates a 30 degree angle at C, which means sin B=1/2, and csc B =2.  This can all be solved, but as a trig student, you should know these special values, and be able to  make the connection when you encounter them.