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Karnataka PUC I Trigonometric Functions — practice questions

Explore 50 free Trigonometric Functions questions in Karnataka PUC I Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Trigonometric Functions questions and exercises with answers

Showing questions 1–30 of 50.

Convert $90^{\circ}$ to radian measure.Read the answer and worked solution →Convert $180^{\circ}$ to radians.Read the answer and worked solution →Convert $360^{\circ}$ to radians.Read the answer and worked solution →Convert $45^{\circ}$ to radian measure.Read the answer and worked solution →Convert $30^{\circ}$ to radian measure.Read the answer and worked solution →Convert $\dfrac{5\pi}{3}$ radians to degree measure.Read the answer and worked solution →Convert $\dfrac{7\pi}{6}$ radians to degree measure.Read the answer and worked solution →Convert $240^{\circ}$ to radian measure.Read the answer and worked solution →In a circle of radius $r$, an arc of length $l$ subtends an angle $\theta$ radian at the centre. The relation is:Read the answer and worked solution →A central angle of $60^{\circ}$ intercepts an arc of length $37.4$ cm in a circle. Find the radius. (Use $\pi = 22/7$.)Read the answer and worked solution →The minute hand of a clock is $1.5$ cm long. How far does its tip travel in $40$ minutes? (Use $\pi = 3.14$.)Read the answer and worked solution →A wheel makes $360$ revolutions in one minute. Through how many radians does it turn in one **second**?Read the answer and worked solution →Equal arcs in two circles subtend angles $65^{\circ}$ and $110^{\circ}$ at the centres. The ratio of the radii $r_{1} : r_{2}$ is:Read the answer and worked solution →What is the value of $\sin 30^{\circ}$?Read the answer and worked solution →What is the value of $\cos 60^{\circ}$?Read the answer and worked solution →What is the value of $\tan 45^{\circ}$?Read the answer and worked solution →What is $\sin 90^{\circ}$?Read the answer and worked solution →What is $\cos 0^{\circ}$?Read the answer and worked solution →What is $\tan 60^{\circ}$?Read the answer and worked solution →What is $\tan 90^{\circ}$?Read the answer and worked solution →$\sin^{2} 45^{\circ} + \cos^{2} 45^{\circ}$ equals:Read the answer and worked solution →The value of $\sin 0^{\circ} + \cos 0^{\circ} + \tan 45^{\circ}$ is:Read the answer and worked solution →If $\sin\theta = \dfrac{3}{5}$ and $\theta$ is in the first quadrant, what is $\cos\theta$?Read the answer and worked solution →What is the **range** of the function $f(\theta) = \sin\theta$?Read the answer and worked solution →What is the **range** of $f(\theta) = \cos\theta$?Read the answer and worked solution →The relationship between degree measure and radian measure is:Read the answer and worked solution →In a circle of radius r, an arc of length l subtends a central angle θ (in radians) such that:Read the answer and worked solution →For all real x, the value of sin²x + cos²x is:Read the answer and worked solution →Convert 40°20′ to radian measure.Read the answer and worked solution →A wheel makes 360 revolutions in one minute. Through how many RADIANS does it turn in one second?Read the answer and worked solution →

Worked practice questions

Convert $90^{\circ}$ to radian measure.

$\dfrac{\pi}{4}$
$\dfrac{\pi}{3}$
$\pi$
$\dfrac{\pi}{2}$

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Correct answer: D. $\dfrac{\pi}{2}$

**Conversion:** $\theta_{\text{rad}} = \dfrac{\pi}{180^{\circ}} \theta_{\text{deg}}$. **So $90^{\circ} = \dfrac{\pi}{180} \cdot 90 = \dfrac{\pi}{2}$.**

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Convert $180^{\circ}$ to radians.

$\dfrac{\pi}{4}$
$\dfrac{\pi}{2}$
$\pi$
$2\pi$

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Correct answer: C. $\pi$

$180^{\circ}$ is a straight angle = $\pi$ radians. **The fundamental relation:** $\pi$ rad = $180^{\circ}$.

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Convert $360^{\circ}$ to radians.

$\pi$
$\dfrac{3\pi}{2}$
$4\pi$
$2\pi$

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Correct answer: D. $2\pi$

One full revolution = $2\pi$ radians.

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