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IRISSAK [1]
3 years ago
14

Determine the image of the point (1, 5) under a rotation of 180° about the origin

Mathematics
1 answer:
klemol [59]3 years ago
6 0
( - 5 , - 1 )

the rotation is just change it into negative
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Prove the following identity :<br>Sin α . Cos α .<br> Tan α =  (1 – Cos<br> α)  (1 + Cos<br> α)
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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 !





4 0
3 years ago
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If B = A , where on the number line will B appear ?
Wittaler [7]
B is going to be where A is
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3 years ago
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