Unit 1 - Mathematics for engineering Flashcards
Mathematics exam for engineering - January 8th
logM + logN = ?
log (MN)
logM - logN = ?
log(M/N)
K logM = ?
log(M^K)
log(1) =
0
logB(B^K) =
log(K)
LogB(B) =
1
ln a + ln b =
ln ab
ln e =
loge(E) = 1
What is y radians in degrees?
(180/ pi) x y
What is y degrees in radians?
(pi/ 180) x y
What is 45 degrees in radians and why?
45 degrees = pi/4
This is because 360 degrees = 2pi radians. So 180 degrees is one pi and 180/45 = 4 which is equal to pi/4.
What is the equation for arc length in degrees?
(θ/350) x 2 x pi x r
What is the equation for arc length in radians?
θ x r
What is the equation for area of a sector in degrees?
(θ/360) x pi x r^2
What is the equation for area of a sector in radians?
(1/2) x r^2 x θ
What is the sine rule?
a/ sinA = b/sinB = c/sinC
What is the Cosine rule?
a^2 = b^2 + c^2 - 2bc Cos(A) or Cos(A) = (b^2 + c^2 - a^2)/(2bc)
In which situation do you use the sine or cosine rule?
If you know a side and its opposite angle, use the sine rule. Otherwise use the cosine rule. These rules are used in non-right angled triangles.
How do you find the area of non-right angled triangles when you have SAS?
Use one of the formulas=
Area = (1/2) x b x c x SinA
Area = (1/2) x a x c x SinB
Area = (1/2) x a x b x SinC
