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Expert: - 6/23/2009


Question

Given right Δ ABC with <C = 90°,  a = 12, b = 5 , find the indicated trig
function in simple form :

1.sin A                                
2. cos B
3.sec B                                 
4.csc B
5.tan A                                   
6.cot A

If Given right Δ ABC with <C = 90°  and  sin B = 3/5, find the indicated trig function in simple form :

1.cos B                                  
2. sec A
3. tan A                       
4. cot B

If Given right Δ ABC with <C = 90°  and  cos A = / 3, find the indicated trig function in simple form :

1.  cot A                                    
2. csc B


Answer
It is known that the tan() is the oppositve over the adjacent.
Since side a is opposite angle A, a/b would be the tan(A) and b/a would be the tan(B).

The tan(A) is the only one there.


To compute the cos() would require computing the other side.

The sec() is 1/cos(), so this would require the same thing.

The tan() is the far side over the near side, so it requires computing the far side as well.

The cot(B) would also require knowing the far side.

The one that would be simple to compute would be csc B,
which is 1 / sin B.

Note that 5^2 - 3^2 = 16, and that is the other side square.
That makes the other side 4.

Thus, the cos B = 4/5, sec A = 5/3, tan A = 3/4, and cot A = 4/3.


In this last problem, we are given cos A = /3,
so I will assume that it is supose to be cos A = 1/3.

This means the hypoteneuse is 3 and the near side is 1.
Note that 3^2 - 1^2 = 8, so the other side is root(8).

That means the cot(A) is 1/root(8) and
csc B = sec A = 1 / cos A = 3 / 1.

According to what was given, the csc B would be 3 / .


If there was suppose to be a different number in there,
I await a reply.

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