Question 429856
Suppose alpha (a) is an angle in Quadrant II and beta is an angle in Quadrant III such that sin(a)= 4/5 and cos(b)= -3/4 
A) Find the exact value of cos(a)
B)Find the exact value of sin(b) 

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Given: sin(a)= 4/5 in quadrant II with reference angle a, the angle the hypotenuse makes with the x-axis.
What you have here is a right triangle  with the hypotenuse=5, the vertical leg=4, and the horizontal leg=-3. This is a 3-4-5 right triangle. The vertical leg represents the sin function and since it is above the x-axis in quadrant II, it is positive. The horizontal leg represents the cos function and since it is to the left of the y-axis, it is negative. Therefore, cos a=-3/5

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Given: cos(b)= -3/4 in quadrant III with reference angle b, the angle the hypotenuse makes with the x-axis.
What you have here is a right triangle  with the hypotenuse=4, the vertical leg=sqrt(4^2-3^2)=-sqrt(7), and the horizontal leg=-3.  The vertical leg represents the sin function and since it is below the x-axis in quadrant III, it is negative. The horizontal leg represents the cos function and since it is again to the left of the y-axis, it is also negative.Therefore, sin b=-sqrt(7)/4