IfsinA = 0.6, what is the value oftanA ?
- (a)0.75
- (b)0.8
- (c)1.25
- (d)2.56
Answer
Why
Correct — A. Find cos A from sin A, then divide.
cos²A = 1 − sin²A = 1 − 0.36 = 0.64
cos A = √0.64 = 0.8 (A taken as acute)
tan A = sin A ÷ cos A = 0.6 ÷ 0.8 = 0.75 → option (a).
Triangle check: 0.6 = 3⁄5, so the sides are 3, 4, 5 and tan A = 3⁄4 = 0.75.
Why the others are wrong
- (b)0.8 — 0.8 is cos A, the step before the answer. tan A divides sin A by cos A: 0.6 ÷ 0.8 = 0.75.
- (c)1.25 — 1.25 is 1 ÷ 0.8, which is sec A. Because sin A = 0.6 is smaller than cos A = 0.8, tan A must be below 1.
- (d)2.56 — 2.56 is above 1, but tan A is below 1 whenever sin A < cos A, and here 0.6 < 0.8. Neither 0.6 ÷ 0.8 nor 0.8 ÷ 0.6 is 2.56.
Concept
sin²A + cos²A = 1 turns one trigonometric ratio into all the others. With sin A = 0.6 = 3⁄5, the right triangle is the 3-4-5 triangle: opposite 3, hypotenuse 5, so adjacent 4.
Every ratio can be read off that triangle: cos A = 4⁄5 = 0.8, tan A = 3⁄4 = 0.75, sec A = 5⁄4 = 1.25 and cot A = 4⁄3.
The stem does not say A is acute. In the second quadrant cos A would be −0.8 and tan A would be −0.75. No negative option is offered, so the acute reading is the one intended.
Key facts
- sin²A + cos²A = 1.
- For an acute angle, sin A = 3⁄5 gives cos A = 4⁄5 and tan A = 3⁄4.
- tan A = sin A ÷ cos A, and sec A = 1 ÷ cos A.
Study next
Common traps
- Stopping at cos A = 0.8, which is on offer as option (b).
- Inverting the wrong ratio: 1 ÷ 0.8 = 1.25 is sec A, not tan A.
The same one-ratio-to-another step is 21 Sep 2025, 09:00, Quant Q.19 (sin A = 0.6 and cos A = 0.8 give tan A = 0.75) and 17 Sep 2025, 09:00, Quant Q.14 (sin θ = 12⁄13 gives tan θ = 12⁄5).
With a quadrant stated, 23 Sep 2025, 16:00, Quant Q.18 puts sin A = 3⁄5 in the 2nd quadrant and keys tan A = −3⁄4.
Related PYQs
No directly related past PYQ was found.