Let's determine the
measures of the angles
formed by two heights of an equilateral triangle.
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 !
Hi there!
Here is what the rules says
+ * + = + (Plus times plus = plus)
+*- = - (Plus times minus = minus)
- * - = + (Minus times minus = Plus
- * + = - (minus times plus = minus)
You need to know the rules by heart because you will use it a lot.
So let see how it works with the problem
6 -(-7)
What does the rules say? It says
- * - = plus
So, we gonna use PLUS for the sign
6-(-7) = 6 + 7 = 13
13 is the correct answer.
I hope I helped. Please let me know if you have more questions.
The speed of a bus that travels 250 km in 2 hours is 145 because you have to divide 250 km and 2 hours which gives 145.
Hope this helps:)
Using the slope formula the answer would be 1-(-1)/(-1)-6. The slope would be 2/-7. It would be a negative slope.
