Deal With Your Trigonometry Assignment Like a Pro| 4 Hacks for Rescue
Writing trigonometry assignment is a tedious task in itself, and if you have to flip the pages of the book back and forth to solve it, then it becomes frustrating. But, what if you could solve trigonometry in your head or at a snap of fingers?
Sounds surreal, right?
Well, there are 4 hacks which will make this happen.
Eager much to know about them?
Keep rolling fellas…
HACK1: Trigonometry Ratio With Mnemonics
You must be aware of what mnemonics are, but have you ever considered using them with the trigonometry ratio? If not, here is a simple one for you to learn and implement.
Some People Have Curly Brown Hair Turned Permanently Black.
Wondering how is it even relevant?
Here is how you have to use it:
Some People Have:
S = P / H
i.e., Sinθ = Perpendicular / Hypotenuse
Curly Brown Hair:
C = B / H
i.e., Cosθ = Base / Hypotenuse
Turned Permanently Back:
T = P / B
i.e., Tanθ = Perpendicular / Base
Easy right!
HACK 2: The Super Hexagon
The almighty savior that will help you learn the trigonometric identities is- The Super Hexagon. The list of identities that can be learned from this magical hexagon is given and explained below. But before that, let us learn to build this hexagon
Three easy steps to follow are:
Step 1: Start with TSC
i.e., tanθ = sinθ / cosθ
Step 2: Add the CCS (clock-wise).
i.e., Cotangent (cot is written on the opposite of tan),
Cosecant (csc is placed next), and
Secant (sec is placed last).
Step 3: Write 1 in the centre of the hexagon.
Easy Trick: All ‘co’ prefixed functions are placed towards the right.
Final Output:
Now, let us learn to use this hexagon.
>> Quotient Identity
Move around the clock in either direction, to get the quotient identities. Here is list of identities that you will be able to calculate:
>>Product Identities
If you look closely, you will be able to identify that a function between any two functions is a product of those two functions. And in case the functions are opposite to each other, 1 lies in between of them. Through this, your list of product identity will be ready, like-
sinθ* cscθ = 1
tanθ* cscθ = secθ
sinθ* secθ = tanθ tanθ* cosθ = sinθ
tanθ* cotθ = 1
>>Reciprocal Identities
If you go through the one in the hexagon, you will be able to identify the reciprocal identities. Here is the list of final reciprocal identities that you will get:
sinθ = 1 / cscθ
cosθ = 1 / secθ
cotθ = 1 / tanθ
cscθ = 1 / sinθ
secθ = 1 / cosθ
tanθ = 1 / cotθ
>>Pythagorean Identities
If you travel clockwise in the small triangles that constitute this hexagon, you will be able to find one set of Pythagorean identities in it. And by moving anticlockwise in these triangles, you get another set of these identities.
Set of identities by clockwise calculation of triangles:
sin2θ + cos2θ = 1
1 + cot2θ = csc2θ
tan2θ + 1 = sec2θ
Example of identities by counterclockwise calculation of triangles
1 — cos2θ = sin2θ
HACK 3: Soh-Cah-Toa
If you have to compute sine, cosine, and tangent of an angle, just chant SOH-CAH-TOA. No kidding!
See the wonder behind this chant,
SOH: Sine equals to Opposite over Hypotenuse
i.e., SOH: Sinθ= Opposite / Hypotenuse
CAH: Cos equals to Adjacent over Hypotenuse
i.e., SOH: Cosθ= Adjacent / Hypotenuse
TOA: Tan equals to Opposite over Adjacent
i.e., SOH: Tanθ= Opposite / Adjacent
HACK 4: Cast the Quadrant
If you want to deal with the quadrant related issues of Trigonometry, just remember the mantra of CAST.
Learn more about it…
Starting with bottom right Quadrant and moving anti-clockwise, you will see that how CAST works:
WOAH! Weren’t they just some live saving tricks?
Well, now stop turning the pages back and forth, it is time to stop procrastinating and start on the trigonometry assignment that has been assigned to you.
