By definition of tangent,
tan(2<em>θ</em>) = sin(2<em>θ</em>) / cos(2<em>θ</em>)
Recall the double angle identities:
sin(2<em>θ</em>) = 2 sin(<em>θ</em>) cos(<em>θ</em>)
cos(2<em>θ</em>) = cos²(<em>θ</em>) - sin²(<em>θ</em>) = 2 cos²(<em>θ</em>) - 1
where the latter equality follows from the Pythagorean identity, cos²(<em>θ</em>) + sin²(<em>θ</em>) = 1. From this identity we can solve for the unknown value of sin(<em>θ</em>):
sin(<em>θ</em>) = ± √(1 - cos²(<em>θ</em>))
and the sign of sin(<em>θ</em>) is determined by the quadrant in which the angle terminates.
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We're given that <em>θ</em> belongs to the third quadrant, for which both sin(<em>θ</em>) and cos(<em>θ</em>) are negative. So if cos(<em>θ</em>) = -4/5, we get
sin(<em>θ</em>) = - √(1 - (-4/5)²) = -3/5
Then
tan(2<em>θ</em>) = sin(2<em>θ</em>) / cos(2<em>θ</em>)
tan(2<em>θ</em>) = (2 sin(<em>θ</em>) cos(<em>θ</em>)) / (2 cos²(<em>θ</em>) - 1)
tan(2<em>θ</em>) = (2 (-3/5) (-4/5)) / (2 (-4/5)² - 1)
tan(2<em>θ</em>) = 24/7
Y=1/2x+c
0=1/2 (10)+c
0=5+c
c=-5
the equation is y=1/2x+5
the slope is the same since these two lines are parallel
Answer:
we need to see the picture or diagram that corresponds to these problems
Step-by-step explanation:
I cant help you unless I see the picture/diagram that corresponds to these problems
So to solve this you need to reverse factor this problem
x^2 + 8x + 7 = 0
The common formula is this for factoring ax^2 + bx + c
Now you have to think what multplties to "c" and adds up to "b".
So in this case it's 7 x 1 = 7 and 7 + 1 = 8
So you set it up like this
(x + 7)(x + 1) = 0
So now you can check the factors by multiplying them together and see if it gets your original equation which is does.
So finally to get the answers you need to set each parenthesis to 0 and solve for x.
x + 7 = 0
x + 1 = 0
and we get x = -1 and - 7
You can also plug these two answers back into your original equation to see if it equals 0.
If you have any questions please feel free to comment
Answer:
Therefore 20 degree is in First Quadrant,
i.e Quadrant I.
Step-by-step explanation:
QUADRANT:
When the terminal arm of an angle starts from the x-axis in the anticlockwise direction then the angles are always positive angles.
Quadrant I - 0° to 90°
Quadrant II - 90° to 180°
Quadrant III - 180° to 270°
Quadrant IV - 270° to 360°
Therefore 20 degree is in First Quadrant, i.e Quadrant I.
When the terminal arm of an angle starts from the x-axis in the clockwise direction than the angles are negative angles.
Quadrant IV - 0° to -90°
Quadrant III - -90° to -180°
Quadrant II - -180° to -270°
Quadrant I - -270° to -360°
