Question 234117: TRIGONOMETRIC FUNCTIONS
1.Given that sin0=4/5 and 0 lies in quadrant ll,find the following value, cos 0
2.Given that sin0=3/5 and 0 lies in quadrant ll,find the following value,sec 0
3.Given that sin=-1/2 and 0 lies in quadrant lV,find the following value,cos 0
4.Given that sin0=-1/2 and 0 lies in quadrant lV, find the following value,tan 0
Answer by nyc_function(2741)   (Show Source):
You can put this solution on YOUR website! BIG TIP: Post one question at a time or else no one will reply.
1.Given that sin0=4/5 and 0 lies in quadrant ll,find the following value, cos 0.
The first thing to know is that the sine function is positive in quadrant 2 but the cosine function is negative in that quadrant.
Also, sine = opposite/hypotense and cosine = adjacent/hypotenuse.
So, sin (0) = 4/5 means that the opposite side of this right triangle in quadrant 2 is 4 and its hypotenuse is 5. We now use the Pythagorean Theorem to find the other leg of the right triangle.
(4)^2 + (leg)^2 = (5)^2
16 + (leg)^2 = 25
(leg)^2 = 25 - 16
(leg)^2 = 9
leg = 3
Now, that we know the other leg of the right triangle is 3, we use that information to find cos (0).
Like I said above, cosine = adjacent/hypotenuse.
Then, cos(0) = 3/5.
However, since cosine is negative in quadrant 2, the answer is cos(0) = -3/5
Follow this same logic to answer the rest of your questions or post one question at a time.
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