Gujarat Board GSEB Textbook Solutions Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.2 Textbook Questions and Answers.

Gujarat Board Textbook Solutions Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.2

Find the values of the other five trigonometric functions in questions 1 to 5:
1. cos x = – (frac{1}{2}), x lies in third quadrant.
2. sin x = (frac{3}{5}), x lies in second quadrant.
3. cot x = (frac{3}{4}), x lies in third quadrant.
4. sec x = (frac{13}{5}), x lies in fourth quardrant.
5. tan x = – (frac{5}{12}), x lies in the second quadrant.
Solutions to questions 1 – 5:
1. Since x lies in the 3rd quadrant, therefore
cos x = – (frac{1}{2}) ⇒ (frac{OM}{OP}) = (frac{- 1}{2}).
Let OM = – 1 and OP = 2.
∴ MP = (sqrt{mathrm{OP}^{2}-mathrm{OM}^{2}}) = – (sqrt{4 – 1}) = – (sqrt{3})

2. Since x lies in the second quadrant, therefore
sin x = (frac{3}{5}) ⇒ (frac{MP}{OM}) = (frac{3}{5})
Let MP = 3, S0, OP = 5.

3. Since x lies in third quadrant, therefore
cot x = (frac{3}{4}) = (frac{- 3}{- 4})
Let MP = – 4. So, OM = – 3. Then,

4. Since x lies in fourth quardrant, therefore
sec x = (frac{13}{5}) ⇒ (frac{OP}{OM}) = (frac{13}{5}) [Given]
Let OP = 13. So, OM = 5. Then,

5. x lies in the second quadrant

Questions?
Find the values of the following trigonometric ratios:
6. sin 765°
7. cosec (- 1410°)
8. tan (frac{19π}{3})
9. sin ((frac{-11π}{3}))
10. cot ((frac{-15π}{4}))
Solutions to questions 6 – 10:
6. sin 765° = (8 × 90° + 45°)
= sin 45° = (frac{1}{sqrt{2}}).

7. cosec (- 1410°) = – cosec 1410° [∵ cosec (-θ) = – cosec θ
= – cosec (16 × 90° – 30°)
= – cosec (- 30)° = – [- cosec 30°]
= cosec 30° = 2.

8. tan (frac{19π}{3}) = tan (6π + (frac{π}{3})) = tan (frac{π}{3}) = (sqrt{3}).

9. sin ((frac{- 11π}{3})) = – sin (frac{11π}{3}) [∵ sin(-θ) = – sin θ]
= – sin(4π – (frac{π}{3})) = – (- sin (frac{π}{3}))
= sin (frac{π}{3}) = (frac{sqrt{3}}{2}).

10. cot((frac{- 15π}{4})) = – cot (frac{15π}{4}) [∵ cot(-θ) = – cot θ]
= – cot (4π – (frac{π}{4})) = – cot (- (frac{π}{4}))
= – (- cot (frac{π}{4})) = cot (frac{π}{4}) = 1.