Trigonometry (Basic) | Learn Mathematics Online

Trigonometry (Basic)

Study Material (PDF)

Study Material (PDF)

Click on each question to see answer & solution.

Question No: #21

The difference between the two acute angles of a right angled triangle is `\frac{2\pi}{5}` radians. Express the value of angles in degree and radian.

Ans: `9^\circ = \frac{\pi}{20}^c`, `81^\circ = \frac{9\pi}{20}^c`

Question No: #22

If the ratio of angles of a triangle is `2:5:3`, then find the value of smallest angle of this triangle in circular measure.

Ans: `\frac{\pi}{5}^c`

Question No: #23

(i) If the two angles of a triangle are `39°2′56′′` and `35°57′4′′`, then find the circular measure of the remaining angle.
(ii) If the two angles of a triangle are `65°56′55′′` and `64°3′5′′`, then find the circular measure of the remaining angle.

Ans: (i) `\frac{7\pi}{12}^c`, (ii) `\frac{5\pi}{18}^c`

Question No: #24

If the ratio of three consecutive angles of a cyclic quadrilateral is `1:2:3`, what are the values of the first and third angles?

Ans: `45^\circ, 135^\circ`

Question No: #25

The circular value of each interior angle of a regular hexagon is -
(a) `\pi/3`, (b) `{2\pi}/3`, (iii) `\pi/6`, (iv) `\pi/4`

Ans: (b) `{2\pi}/3`

Question No: #26

If the difference of each interior and exterior angle of a regular polygon is 108°, then find the value of each interior angle in circular measure.

Ans: `\frac{4\pi}{5}^c`

Question No: #27

If `\alpha + \beta = 90^\circ` and `\alpha : \beta = 2:1`, the value of `sin \alpha : sin \beta` is -
(a) `3:1`, (b) `1:3`, (c) `\sqrt{3}:1`, (d) `1:\sqrt{3}`

Ans: (c) `\sqrt{3}:1`

Question No: #28

In `triangle`ABC, if `sin (A+B) = \sqrt{3}/2`, then the value of `cos \frac{C}{2}` is .........

Ans: `1/2`

Question No: #29

If `tan (\theta + 15^\circ) = \sqrt{3}`, then find the value of `(sin \theta + cos \theta)`.

Ans: `\sqrt{2}`

Question No: #30

If `sin (\theta - 30^\circ) = 1/2`, then value of `cos \theta` is ........

Ans: `1/2`

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