This is the rule of sums of trig identities. It says that sin(a + b) = sina*cosb+sinb*cosa. Set up your right triangles. In a 30-60-90 triangle, the side across from the 60 angle is the square root of 3, the side across from the 30 is 1, and the hypotenuse is 2. In a 45-45-90 the sides across from the 45 degree angles are 1 and the hypotenuse is square root of 2. With that being said, the sin of 60 is 
and the cos of 60 is 1/2. Both the sin and cos of 45 is 
. So your formula is filled in like this: 
. When you do the multiplication on those sets of parenthesis, you get 
. When you add those your solution is 
. Depending upon your instructor you may have to rationalize that denominator to get that radical out from under there, but if not, that's pretty much it!
Which system of equations has two solutions?
2 answers:
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Answer:
Volume of the prism is 648
Step-by-step explanation:
Given:
Base of the prism is rectangular in shape
Height of the prism = 6 cm
Base length of the prism= 12 cm
Base width of the prism= 9 cm
To Find:
Volume of the prism=?
Solution:
Volume of the prism ,
V= Base area of the prism x Height of the prism
Here in the figure base of the prism is in Rectangular form
So the base area of the prism = area of the rectangle
We know that the area of the rectangle is = length x height
Substituting the values
Area of the Rectangle = 12 x 9
Area of the Rectangle = 108
So the are of the base of the prism is 108
Now
Volume of the prism,
V= 108 X 6
V= 648
