<span>
6 Find an exact value. sin 75°
</span>sin(A+B)=sin(A)cos(B)+cos(A)sin<span>(B)
</span>sin(45)=cos(45)=(2^0.5)/2 sin(30)=0.5 cos(30)=(3^0.5)/2
sin(45+30)=sin(45)cos(30)+cos(45)sin(30)=(6^0.5+2^0.5)/4
the answer is the letter d) quantity square root of six plus square root of two divided by four.
<span>
7. Find an exact value. sine of negative eleven pi divided by twelve.
</span>sin(-11pi/12) = -sin(11pi/12) = -sin(pi - pi/12) = -sin(pi/12) = -sin( (pi/6) / 2)
= - sqrt( (1-cos(pi/6) ) / 2) = -sqrt( (1-√3/2) / 2 ) = -(√3-1) / 2√2=(√2-√6)/4
the answer is the letter c) quantity square root of two minus square root of six divided by four.
<span>
8. Write the expression as the sine, cosine, or tangent of an angle. sin 9x cos x - cos 9x sin x
</span>
sin(A−B)=sinAcosB−cosAsinB
sin(9x−x)= sin9xcosx−cos9xsinx= sin(8x)
the answer is the letter c) sin 8x
<span>
9. Write the expression as the sine, cosine, or tangent of an angle. cos 112° cos 45° + sin 112° sin 45°</span>
cos(A−B)=cosAcosB<span>+sinA</span>sinB
cos(112−45)=cos112cos45<span>+sin112</span>sin45=cos(67)
the answer is the letter d) cos 67°
10. Rewrite with only sin x and cos x.
sin 2x - cos 2x
sin2x =
2sinxcosx<span>
cos2x = (cosx)^2 - (sinx)^2 = 2(cosx)^2 -1 = 1- 2(sinx)^2</span>
sin2x- cos2x=2sinxcosx-(1- 2(sinx)^2=2sinxcosx-1+2(sinx)^2
sin2x- cos2x=2sinxcosx-1+2(sinx)^2
<span>
the answer is the letter <span>
b) 2 sin x cos2x - 1
+ 2 sin2x</span></span>
Answer:
Step-by-step explanation:
Answer:
(-5, 1)
Explanation:
We are given a kite on the graph which is rotated 180° clockwise about the origin and then reflected over the Y axis followed by reflection over the X axis.
We are to find the coordinates of point A after the complete transformation.
A (-5, 1)
When a point is rotated 180° clockwise about the origin, the signs of its coordinates change.
A (-5, 1) ---> A' (5, -1) - after clockwise rotation of 180 degrees about origin
Then this point A' is reflected over the Y axis where the y coordinate remains the same but x coordinate changes its sign.
A' (5, -1) ---> A'' (-5, -1) - after reflection through y axis
Now this point A'' is reflected over the X axis where the x coordinate remains the same while y coordinates changes its sign.
A'' (-5, -1) ---> A''' (-5, 1) - after complete transformation
A.
I=prt
I=(3800)(.055)(4/12)
I=$69.67
b.
Principal-interest=money received from Bank
3800-69.67=$3730.34
c.
I=prt
69.67=3730.34(r)(4/12)
69.67=1243.45r
69.67/1243.45=1243.45/1243.45r
.056≈r
Rate is 5.60%
34/100
= 0.34
3 tenths, 4 hundreths
Answer:
-24.8 m/s
Step-by-step explanation:
Given:
y₀ = 60 m
y = 40 m
v₀ = 15 m/s
a = -9.8 m/s²
Find: v
There are three constant acceleration equations we can use:
y = y₀ + v₀ t + ½ at²
v = at + v₀
v² = v₀² + 2a(y − y₀)
We aren't given the time, so we need to use the third equation, which is independent of time:
v² = v₀² + 2a(y − y₀)
Plug in the values:
v² = (15 m/s)² + 2(-9.8 m/s²) (40 m − 60 m)
v² = 617 m²/s²
v ≈ ±24.8 m/s
Since the coin is on the way down, the velocity is negative. So v = -24.8 m/s.
