[Trigonometry] Type#2: Table based questions, memorization technique, approach explained for SSC CGL

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  1. Introduction
  2. Table based Questions
  3. Case1: finding value
  4. Case2: multiplication chain
  5. Case3: finding angle
  6. Mock Questions

Introduction

For SSC CGL trigonometry, there are mainly four types of questions

  1. Height and distance: and it has five subtypes. We already saw how to solve them. If you haven’t seen it, click on my youtube playlist
  2. Table based: Finding values and angles: We will see this in today article.
  3. Complimentary angles (90-A): discussed in separate article click me.
  4. Trigonometry formulas + algebraic formulas: to be released.

Table based Questions

Here is an example of Table based questions:

  1. What is the value of 3cos230+sec230+2cos-+3sin90-tan290
  2. If sinA=2sin30*cos30, then find value of A
  • To solve these type of questions, you must know the “table” (=meaning the values of sin, cos, tan, cosesc, sec and cot for 0, 30, 45, 60 and 90 degree angles).
  • From the earlier youtube video, you already know the shortcut technique to memorize the values of 30, 45, 60 of sin, cos, tan, cosec, sec, cot, using those two “topi triangles”. (if not click me)
  • Today we’ll extend it further and create the whole table from 0 to 90 degrees.
0 30 45 60 90
Sin
Cos
Tan
Cosec
Sec
cot

topi triangles
First using above “Topi triangles” I’m going to fill up the values of Sin, cos, tan for 30, 45 and 60 degree angles. (sin = opp/hypo, cos=adj/hypo and tan=opp/adj)

trig table only 3 30-60
but we know know that

  1. sin = 1/ cosec. That means for cosec 0 to 90, I’ll just inverse the values of sin 0 to 90. (e.g. sin30=1/2 means cosec30 will equal to 2)
  2. Cos=1/sec. that means for sec 0 to 90, I’ll just inverse the values of cos 0 to 90. (e.g. cos60=1/2 therefore sec60=2).
  3. Tan=1/cot. That means for cot 0 to 90, I’ll just inverse the values of tan 0 to 90 (e.g. tan45=1, so cot45 will also be 1).

Here is the updated table. (don’t just read this, keep making the table in your notebook/rough paper simultaneously).

trig table all 6 30-60
Ok so far, we’ve filled up all the values for 30, 45 and 60. Only two column remain: 0 degree and 90 degree. That can be filled up very quickly if you just remember two things

  1. For zero to ninety, sin is 0 to 1. And the case of cos is reverse (meaning for zero to ninety, cos is 1 to 0).
  2. Zero’s inverse (1/0)=not defined. And vice versa (meaning “1/not defined” = 0).
  • Applying the first rule: for 0 to 90, sin is 0 to 1, and cos is 1 to 0.
    • WE also know that Tan=sin/cos.
    • So tan0=0/1=0 and
    • tan90=1/0=Not defined
  • now we’ve the values of sin, cos and tan for 0 degree angle and 90 degree angle. We can inverse them and get the values for cosec, sec and cot also. (recall rule number two: 1/0=not defined and not defined’s inverse is 0).

Finally we’ve our table ready.

trig table 0-90
I suggest you construct this table on your own for atleast 2-3 times at home. Otherwise this technique will not go in long term memory.
In the exam you don’t have to create the whole table in the rough paper, just get only those values that are required for the given question. Now let’s try some Table based Questions.

Case1: finding value

Q. Find value of sin60*sin45+cos60*cos45

  • Just Plug in the values into the given equation
  • Answer will be (root6+root2)/4

Q. if cosA+cosB=2 then find value of sinA+SinB, given that both angle A and B are between 0-90 including both 0 and 90.

  • Ans. If you look at the table, cos0+cos0=1+1=2. That means both A and B angles are 0 degree angles.
  • Therefore SinA+SinB=Sin0+sin0=0+0=0.

Q. Find the value of cos25/sin65.

  • We only know the table for 0, 30,45,60 and 90. We don’t know the tables for 25 or 65. Don’t worry, these questions are based on the formula of complimentary angles. We’ll learn that in next article.

Case2: multiplication chain

Q. find the value of tan0 x tan1 x tan2 x tan3x….tan89

Approach: from the table we know that tan0=0. So no matter what you multiply with zero, final answer will always be zero.

Q. find the value of cos2 x cos4 x cos6 x cos8x….x cos92

Approach: as you can see the angles are increasing as per the multiplication table of 2. So in the chain, you’ll also get cos90 (because 2 x 45=90). So we can write the chain as

cos2 x cos4 x cos6 x cos8x….cos88 x cos90 x cos92

but we know that cos90=0, hence the whole multiplication will become zero.

Q. find the value of tan48 x tan 23 x tan 42 x tan67

Approach: as you can see there is no tan0 in this multiplication chain (otherwise we could get zero as the answer.) but this question can be easily solved using the formula of complimentary angles. (we’ll see it in the next article).

Case3: finding angle

Q. For 0<A<90, if sinA=sin60 x cos30-cos60 x sin30, then what is the value of A?

  1. 0
  2. 30
  3. 45
  4. 90

Approach:

left hand side LHS right hand side RHS
sinA= sin60 x cos30-cos60 x sin30
Plug in the values and you get right hand side is 1/2
sinA= 1/2

Now go back and observe the table. In the Sin’s row, You see the sin30=1/2. Therefore, A=30 degrees.

Q. If Sin(A+B)=root3/2 and SIN(A-B) =1/2 then what are the values of A and B? (given that both A and B are acute angles and A>B)

  1. 30,60
  2. 45,45
  3. 45,15
  4. None of above.

Approach

  • Sin(A+B)=root3/2 (this is given in the question itself).
  • If you look at the table, sin60=root3/2. That means A+B=60…eq1
  • Similarly we’ll get A-B=30….eq2
  • So we’ve two equations:
  • A+B=60
  • A-B=30
  • Now add these two equations eq1+eq2
  • (A+B)+(A-B)=60+30
  • 2A=90
  • A=45
  • Plug this value back in eq1 (or eq2). And you get B=15
  • Final answer C: 45,15

Mock Questions

Instructions

  • For all these questions, assume that unknown angles are between 0 to 90 (including both 0 and 90).
  • Questions about finding values (based on trigonometry table) are easy. You just have to plug in the values and simplify the equation.
  • But be sure to observe the rules of simplification (BODMAS) and laws of surds and indices, else you’ll get wrong answer.
  1. if CosA=1-2sin230, then find value of A
    1. 30
    2. 45
    3. 60
    4. 90
  2. if cosA=2cos230-1, then find value of A
    1. 30
    2. 45
    3. 60
    4. 90
  3. if cos60=cos2A-sin230, then find value of A
    1. 60
    2. 45
    3. 30
    4. 90
  4. if sinA=2sin30*cos30, then find value of A
    1. 30
    2. 45
    3. 60
    4. 90
  5. if sinA=2tan30/ (1+tan230), then find value of A
    1. 30
    2. 45
    3. 60
    4. 90
  6. if cosA=(1-tan230)/( 1+tan230), then find value of A
    1. 30
    2. 45
    3. 60
    4. 90
  7. if cosA=4cos330-3cos30, then find value of A
    1. 30
    2. 45
    3. 60
    4. 90
  8. Find value of (5cos260+4sec230-tan245)/(sin230+cos230)
    1. 67
    2. 12
    3. 67/12
    4. 12/67
  9. Find value of 3cos230+sec230+2cos0+3sin90-tan260
    1. 67
    2. 12
    3. 67/12
    4. 12/67
  10. If sinA=cosA, what is the value of 2tan2A+sin2A+1
    1. 2
    2. 7
    3. 7/2
    4. 2/7
  11. What is the value of sinA*cosB+cosA*sinB, if A=30 and B=60
    1. 0
    2. 1/2
    3. 2
    4. 1
  12. What is the value of cosAcosB-sinAsinB, if A=30 and B=60
    1. 0
    2. 1/2
    3. 2
    4. 1
  13. secA=cosec60, what is the value of 2cos2A-1
    1. 0
    2. 1/2
    3. 2
    4. 1
  14. What is the value of 5cos290+3sec230+4cos245+tan260
    1. 3
    2. 7
    3. 5
    4. 9
  15. What is the value of 5cos90-cot30+(sin60/cos245)
    1. 1
    2. 3
    3. 0
    4. 5
  16. Find the value of (cos30+sin60)/(sin30+cos60+1)
    1. 1/2
    2. 1/root2
    3. Root3/2
    4. 2/root3
  17. Find the value of tan260/(sin245+cos245)
    1. 3
    2. 1/2
    3. 2/3
    4. 1/3
  18. If cot(A+B)=1/root3 and Cot(A-B)=root3. Find the values of A and B
    1. 30,60
    2. 60,30
    3. 15,45
    4. 45,15
  19. Find the value of cos10 x cos20 x cos30 x….x cos90
    1. 1
    2. 1/2
    3. 0
    4. Not defined.
  20. If secA-cosecA=0 then find value of secA+cosecA, given that A is an acute angle.
    1. Root 2
    2. 2 root 2
    3. 0
    4. Not defined

Answers

1)c, 2)c, 3)c, 4)c, 5)c, 6)c, 7)d, 8)c, 9)c, 10)c, 11)d, 12)a, 13)b, 14)d, 15)c, 16)c, 17)a, 18)d, 19)c, 20)b

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