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)
(a stands for alpha and b for beta)
I didn't exactly comprehend my teacher's explanation so any help will help me a lot. Thanks in advance if anyone helps. (also, sorry if this is cramming too many problems....?)
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! 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)
..
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
..
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
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