Answer:
41 Degrees
Step-by-step explanation:
So basically you add the 72 and the other 72 to get 148.You obviously know the angle in between 72 and 72 is a right angle or 90 degrees.Then you add 148 and 90 to get 238.Then 360 - 238 is 122.Now you know all the angles.So we have to ask ourselves what is 148/360 simplified.It is 37/90.Now that we know that and we know that the radius is 10.We have to find the regular area which is 10 times 10 which is 100.Finally we need to figure out what part of 100 is 37/90 and it is 41.111111111111.Rounded it is 41.
Let's work on the left side first. And remember that
the<u> tangent</u> is the same as <u>sin/cos</u>.
sin(a) cos(a) tan(a)
Substitute for the tangent:
[ sin(a) cos(a) ] [ sin(a)/cos(a) ]
Cancel the cos(a) from the top and bottom, and you're left with
[ sin(a) ] . . . . . [ sin(a) ] which is [ <u>sin²(a)</u> ] That's the <u>left side</u>.
Now, work on the right side:
[ 1 - cos(a) ] [ 1 + cos(a) ]
Multiply that all out, using FOIL:
[ 1 + cos(a) - cos(a) - cos²(a) ]
= [ <u>1 - cos²(a)</u> ] That's the <u>right side</u>.
Do you remember that for any angle, sin²(b) + cos²(b) = 1 ?
Subtract cos²(b) from each side, and you have sin²(b) = 1 - cos²(b) for any angle.
So, on the <u>right side</u>, you could write [ <u>sin²(a)</u> ] .
Now look back about 9 lines, and compare that to the result we got for the <u>left side</u> .
They look quite similar. In fact, they're identical. And so the identity is proven.
Whew !
Answer:
Step-by-step explanation:
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