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If we consider what the distance formula really tells you we can see the similarities. It is more than just a similar form. The distance formula […]

Remember that ##cos2theta=1-2sin^2theta##. Hence ##1-2sin^2(2x)=cos4x##

##D * d## ABCE. the diagonals AC and BE are perpendicular. Area of ##Delta ABC = 1/2 * D * d = ## Area of ##Delta […]

Use the trig identity: ##sin (a – b) = sin a.cos b – sin b.cos a## ##sin (60 – x) = sin 60.cos x – cos […]

##sec(cos^(-1)(1/2)) = 2## Another way without calculating ##cos^(-1)(1/2)##: Consider a right triangle with an angle ##theta = cos^(-1)(1/2)##. Then ##cos(theta) = 1/2## meaning the ratio of […]

You probably know that ##180## corresponds to ##pi## radians; You can build the proportion: ##180:pi=():(rad)## Set ##()=-220## and solve for ##(rad)##; you’ll get: ##(rad)=-220pi/(180)=-22pi/(18)=-11/9pi##

The area of such rectangle is ##60##. Using the ##a^2+b^2=c^2## we substitute the expressions into the equation: ##x^2+(2x+2)^2=13^2## ##x^2+4x^2+8x+4=169## ##5x^2+8x-165=0## Factor the equation: ##(5x^2-25x)+(33x-165)=0## ##5x(x-5)+33(x-5)=0## ##(5x+33)(x-5)=0## […]

##2 26/45## ##meters## First convert the mixed numbers into improper fractions. ##area=5 4/5=5+4/5=25/5+4/5=29/5## ##width=2 1/4=2+1/4=8/4+1/4=9/4## Next we need to know that the area of a rectangle […]

##~~3.37## I changed the points into Cartesian then used the Pythagoras distance equation The distance ##S## between two points on a plane is given by: ##S […]