Question 873823: Currently I am stuck on a sort of basic trigonometry question that I have to do for homework. The question is as follows:
a.Find the values of each pair of expressions.
1.)sin 80°, cos 10°
2.)cos 25°, sin 65°
b. What do you notice about your values and the angles in each pair?
c.Explain why your results make sense.
For A I've found the values which are 0.98 for the first set, and for the second set it is 0.9 for both also. For B, I answered that I noticed for each set they are equal to each other, but I didn't notice anything between the angles. As for C, I'm lost because I don't know why they are equal to each other. If someone can explain the relationships between the angles and all that stuff, I would be really thankful.
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! a.Find the values of each pair of expressions.
1.)sin 80°, cos 10°
2.)cos 25°, sin 65°
b. What do you notice about your values and the angles in each pair?
c.Explain why your results make sense.
***
In both cases 1 and 2, both angles add to 90˚which means the angles are complementary.
Note that both angles have the same value, that is, sin 80˚=cos 10˚, cos 25˚=sin 65˚, which is true for complementary angles. The best way I know how to explain this is with a right triangle.For example, let's take a right triangle where one of the angles is 80˚ so the other must be 10˚.Sin of an angle is defined as side opposite/hypotenuse and cos of an angle side adjacent/hypotenuse.Notice how the opposite side of sin 80˚ becomes the adjacent side cos 10˚function, so both the 80˚ sin and 10˚cos are using the same side over the hypotenuse to end up with equal values. Try an example using 60 and 30 deg, and it might help to make things clearer. All this results in an important identity which you should be very familiar with: sin(90-x)=cosx, and cos(90-x)=sinx
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