Trig question

[icelated]

I have a problem in my text book that i cannot possibly figure out.

if sin(A) = 3/5 and angle A is in the second quadrant, find the following without using any inverse functions. Provide exact answer
completely simplified.

I cannot do
a. b. or c.

a. cos(A)
b. tan(A)
c. csc(A)

I do not even know how to tackle this problem! Do i need to use some type of identity?
How can 3/5 be in Q2?and why does that even matter?
Can someone help me do the first one a. cos(A) and then i can do the rest?

I just dot know where to begin.
Thank you

 

[wjm11]

if sin(A) = 3/5 and angle A is in the second quadrant, find the following without using any inverse functions. Provide exact answer
completely simplified.

Just draw a triangle in the second quadrant with A as the reference angle (near the origin). Remember that the sine of an angle is equal to the ratio of the opposite side over the hypotenuse. Since the sine of A is 3/5, that means that the opposite side is 3 and the hypotenuse is 5. Write these values on your drawing. Using the Pythagorean Theorem, we can calculate that the adjacent side is 4. However, since this is in the second quadrant, that 4 is in the negative x direction, so it is a -4. (That's why the quadrant matters; we have to keep track of the signs of the x and y values.) Mark that on your drawing also.

Now that you have all three sides of the triangle solved, you can find any trig ratio that you want for angle A.

 

[icelated]

Oh, i should have known this.

Remember that the sine of an angle is equal to the ratio of the opposite side over the hypotenuse.

what if the angle is in degrees?

I guess i am use to working in the other direction. Not backwards.. Thank you..


a) cos(A) = 4/3

Since, tan(A) = sin / cos
b) tan(A) = 3/ -4?
c) csc = 1 / sin = 1/3?

Thank you

 

[wjm11]

what if the angle is in degrees?

a) cos(A) = 4/3

Since, tan(A) = sin / cos
b) tan(A) = 3/ -4?
c) csc = 1 / sin = 1/3?

We don't really care what the angle is in this problem; it irrelevant whether it's in degrees or not.

cos(A) = -4/5 (adjacent/hyp.)
tan(A) = 3/ -4 = -(3/4)
csc(A) = 1 / sin(A) = 1/(3/5) = 5/3