Simple way to see it is to multiply the value opposite of the axis you're flipping it over by -1. For example the point (-5,7) would become (5,7) when reflected over the y-axis, because the point is moving from the left to the right. This means the triangle would be (1,3) (5,3) and (5,7) when reflected over the y-axis. For reflection over the x-axis it would be (-1,-3) (-5,-3) and (-5,-7) because each point is moving down.
Find <span>tan<span>(<span><span>5π</span>12</span>)</span></span> and sin ((5pi)/12)
Answer: <span>±<span>(2±<span>√3</span>)</span>and±<span><span>√<span>2+<span>√3</span></span></span>2</span></span>
Explanation:
Call tan ((5pi/12) = t.
Use trig identity: <span><span>tan2</span>a=<span><span>2<span>tana</span></span><span>1−<span><span>tan2</span>a</span></span></span></span>
<span><span>tan<span>(<span><span>10π</span>12</span>)</span></span>=<span>tan<span>(<span><span>5π</span>6</span>)</span></span>=−<span>1<span>√3</span></span>=<span><span>2t</span><span>1−<span>t2</span></span></span></span>
<span><span>t2</span>−2<span>√3</span>t−1=0</span>
<span>D=<span>d2</span>=<span>b2</span>−4ac=12+4=16</span>--> <span>d=±4</span>
<span>t=<span>tan<span>(<span><span>5π</span>12</span>)</span></span>=<span><span>2<span>√3</span></span>2</span>±<span>42</span>=2±<span>√3</span></span>
Call <span><span>sin<span>(<span><span>5π</span>12</span>)</span></span>=<span>siny</span></span>
Use trig identity: <span><span>cos2</span>a=1−2<span><span>sin2</span>a</span></span>
<span><span>cos<span>(<span><span>10π</span>12</span>)</span></span>=<span>cos<span>(<span><span>5π</span>6</span>)</span></span>=<span><span>−<span>√3</span></span>2</span>=1−2<span><span>sin2</span>y</span></span>
<span><span><span>sin2</span>y</span>=<span><span>2+<span>√3</span></span>4</span></span>
<span><span>siny</span>=<span>sin<span>(<span><span>5π</span>12</span>)</span></span>=±<span><span><span>√<span>2+<span>√3</span></span></span>2</span></span></span>
Answer:
Explanation:
Use the Pythagorean theorem (
a
2
+
b
2
=
c
2
)
Lets label the right triangle such that:
a
=
12
b
=
16
c
=
x
Thus,
12
2
+
16
2
=
x
2
144
+
256
=
x
2
400
=
x
2
√
400
=
x
20
=
x
So our missing side,
c
is
20
We can now say that the sides of our triangle are
12
,
16
,
20
I've included a link that lists a couple of Pythagorean triples (a couple because they are infinitely many).
Step-by-step explanation:
Hope it helpful
Answer:
1 2/3 = 5/3
6 3/4 = 27/4
-9 7/3 = -34/3
4 2/7 = 30/7
Step-by-step explanation:
