Math

Question 1

Trigonometric ratio mnemonic from a known angle

Answer 1

soh cah toa

sine = opposite/hypotenuse cosine = adjacent/hypotenuse tangent = opposite/adjacent

Question 2

Factoring a sum of cubes

a³ + b³

x³​+ 1

Answer 2

Formula: (a+b)(a2-ab+b2)

a3 + b3 = (a+b)(a2-ab+b2)

x3 + 1 = (x + 1)(x2-1x+1²)

Question 3

Cosecant

csc(x) =

Answer 3

Reciprocal of sine

csc(x) = 1/sin(x)

csc = hypotenuse/opposite side

Question 4

Secant

sec(x) =

Answer 4

Receiprocal of cosine

sec(x) = 1/cos(x)

sec = hypotenuse/adjacent side

Question 5

Cotangent

cot(x) =

Answer 5

The reciprocal of tangent

cot(x) = cos(x)/sin(x)

cot = adjacent/opposite side

Question 6

sec(0) =

Answer 6

1

Question 7

What is a natural log?

ln

Answer 7

The natural logarithm of a number is its logarithm to the base e, where e is an irrational and transcendental constant approximately equal to 2.718281828.

Question 8

What is relationship of tangent with cosine, and sine?

Answer 8

tan = sin/cos

Question 9

1/(2/5) =

Answer 9

5/2

Question 10

What is a similar triangle?

Answer 10

Corresponding angles are congruent (equal). One triangle is simply a scaled (up/down) version of the other. All sides are scaled by the same factor.

(Denoted: Triangle ABC _~ Triangle DEF)

Question 11

Negative exponents

4^-3 = ?

Answer 11

1/4³ = 1/64

You take the reciprocal of the coefficient to the positive exponent. [e.g. (3/2)^-2 = (2/3)²]

Question 12

Fractional Exponents

4^1/2 = ?

Answer 12

sqrt(4) = 4^1/2

(or cube root of 8 = 8^1/3)

Question 13

Multiplying values with exponents.

x⁵* x³ = ?

Answer 13

Add the exponents

x⁵⁺³ = x⁸

Question 14

Raising an exponent

(3^a)⁵ = ?

Answer 14

Multiply the exponents

(3^a)⁵ = 3^5a

Question 15

Fractions raised to a power:

(3/2)³ = ?

Answer 15

(3/2)³ = 3³/2³

Question 16

Simplify

(5d)^1/2= ?

Answer 16

(5d)^1/2 = 5^1/2 * d^1/2

It is equivalent to taking each term to that exponent. Same with division.

Question 17

What is the relationship between sine and cosine?

Answer 17

sin x = cos (90-x)

Sine of an angle is equal to cosine of its complementary angle in the right triangle. (sin 32° = cos 58°)

Question 18

Simplify

x^-2/3

Answer 18

x^-2/3 = 1/x^2/3

x^2/3 = (x^2*1/3) = (x²)^1/3

= cubrt(x²)

In other words: denominator root of x to the power of the numerator.