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
Answer:
Let AB is the height of the cliff = H and p is the posit ion of the boat.Angle of depression= angle of elevation= 15 degrees therefore angle APB= 15 degrees tan 15=AB=h/1,000 h=(1,000)*tan 15=(1,000)(0.26794919243112)=268.94919243112 meters or
Simply: 268meters..........Ans
Yo sup??
The two triangles are similar by AAA property ie
Angle Angle Angle property
Let us name the two triangles as ABC and DEF
By observing the figure
mB=mE=90 (right angled triangle)
mA=mD (parallel lines property)
mC=mF (parallel lines property)
Therefore by AAA the two triangles are similar .
The diagram is given below.
PS: All the credits for image goes to Picasso-PSN03
Answer:
5 shirts and 4 pairs of shorts
Step-by-step explanation:
160-1 set (12+25=37)=123
123-1 set=86
86-37=49
49-37=12
12-1 t-shirt=0
Answer:
x = 1
Step-by-step explanation:
12 + 4 x = 16
Subtract 12 from both sides.
4x = 4
Divide 4 on both sides.
x = 1
