<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>
I would consider the number 2
Answer:
5
Step-by-step explanation:
magnitude of the vector
=√(3²+4²)
=√25
=5
Answer: The correct option are (1). c, (2). d and (3). (b).
Step-by-step explanation: The calculations are as follows:
(1) We are to find the solution of the following quadratic equation:
We have
![n^2-49=0\\\\\Rightarrow n^2=49\\\\\Rightarrow n=\pm7~~~~~\textup{[taking square roots on both sides]}](https://tex.z-dn.net/?f=n%5E2-49%3D0%5C%5C%5C%5C%5CRightarrow%20n%5E2%3D49%5C%5C%5C%5C%5CRightarrow%20n%3D%5Cpm7~~~~~%5Ctextup%7B%5Btaking%20square%20roots%20on%20both%20sides%5D%7D)
Thus, the correct option is (c). 
(2) We are to find the solution of the following quadratic equation:
We have
Since there is no real number whose square is negative, so this equation has no solution.
Thus, the correct option is (d). no solution.
(3) We are given to find the side length of a square with an area of 144x².
Let, 'a' denotes the side length of the square.
Then,
![a^2=144x^2\\\\\Rightarrow a=\pm12x.~~~~~~~\textup{[taking square root on both sides]}](https://tex.z-dn.net/?f=a%5E2%3D144x%5E2%5C%5C%5C%5C%5CRightarrow%20a%3D%5Cpm12x.~~~~~~~%5Ctextup%7B%5Btaking%20square%20root%20on%20both%20sides%5D%7D)
Since the length of the side cannot be negative, so the side length is 12x.
Thus, (b) is the correct option.
The correct option are (1). c, (2). d and (3). (b).
