Trigonometry Additional One Mark Online Test

Trigonometry Additional One Mark Online Test (10th Standard Mathematics)

Pick how many questions you want and set a time limit, then start. You'll get your score at the end with the correct answer and an explanation for every question. Free, in Tamil and English — 15 questions available.

Set up your test

Number of questions

Time limit

Time remaining00:00

If \(x = a \\sin \\theta\) and \(y = b \\cos \\theta\), then the value of \(b^2 x^2 + a^2 y^2\) is

A.\(a^2 b^2\) B.\(a^2 + b^2\) C.\(\\frac{a^2}{b^2}\) D.1

If \(\\tan \\theta + \\cot \\theta = 2\), then the value of \(\\tan^2 \\theta + \\cot^2 \\theta\) is

A.4 B.2 C.1 D.0

The value of \((1 + \\cot^2 \\theta)(1 - \\cos \\theta)(1 + \\cos \\theta)\) is

A.1 B.-1 C.\(\\sin^2 \\theta\) D.\(\\cos^2 \\theta\)

If \(\sin \theta = \cos \theta\) for \(0^\circ \le \theta \le 90^\circ\), then the value of \(2\tan^2 \theta + \sin^2 \theta - 1\) is

A.\(\\frac{3}{2}\) B.\(\\frac{1}{2}\) C.1 D.2

If \(\\sec \\theta + \\tan \\theta = x\), then the value of \(\\sec \\theta - \\tan \\theta\) is

A.\(x\) B.\(\\frac{1}{x}\) C.\(x^2\) D.1 - x

If \(\\cos \\theta = \\frac{3}{5}\), then the value of \(\\frac{\\sin \\theta - \\cot \\theta}{2 \\tan \\theta}\) is

A.\(\\frac{3}{160}\) B.\(\\frac{3}{80}\) C.\(\\frac{1}{160}\) D.\(\\frac{1}{80}\)

An observer finds that the angle of elevation of the top of a tower is \(30^\circ\). If the observer moves \(20\) m closer to the tower, the angle of elevation becomes \(60^\circ\). The height of the tower is

A.\(10\\sqrt{3}\) m B.\(20\\sqrt{3}\) m C.\(10\) m D.\(15\) m

The angle of elevation of the top of a building from a point on the ground, which is \(30\) m away from the foot of the building, is \(45^\circ\). The height of the building is

A.\(30\) m B.\(15\) m C.\(30\\sqrt{3}\) m D.\(\\frac{30}{\\sqrt{3}}\) m

If a pole of height \(6\) m casts a shadow of length \(2\\sqrt{3}\) m on the ground, then the angle of elevation of the sun is

A.\(30^\circ\) B.\(45^\circ\) C.\(60^\circ\) D.\(90^\circ\)

Q10

If the angle of depression of an object on the ground from the top of a \(75\) m high tower is \(30^\circ\), then the distance of the object from the foot of the tower is

A.\(75\\sqrt{3}\) m B.\(25\\sqrt{3}\) m C.\(75\) m D.\(150\) m

Q11

If \(\\cos \\theta + \\sec \\theta = 2.5\), then the value of \(\\cos^2 \\theta + \\sec^2 \\theta\) is

A.4.25 B.6.25 C.5.25 D.2.25

Q12

The expression \(\\frac{\\sin^3 \\theta + \\cos^3 \\theta}{\\sin \\theta + \\cos \\theta} + \\sin \\theta \\cos \\theta\) simplifies to

A.1 B.2 C.1 + 2\\(\sin\) \\(\theta\) \\(\cos\) \\(\theta\) D.\(\\sin^2 \\theta \\cos^2 \\theta\)

Q13

If \(\\tan \\theta = \\frac{a}{b}\), then the value of \(\\frac{a \\sin \\theta - b \\cos \\theta}{a \\sin \\theta + b \\cos \\theta}\) is

A.\(\\frac{a^2 - b^2}{a^2 + b^2}\) B.\(\\frac{a^2 + b^2}{a^2 - b^2}\) C.\(\\frac{a - b}{a + b}\) D.1

Q14

A ladder leaning against a vertical wall makes an angle of \(60^\circ\) with the ground. If the foot of the ladder is \(3.5\) m away from the wall, then the length of the ladder is

A.\(7\) m B.\(3.5\\sqrt{3}\) m C.\(14\) m D.\(5\) m

Q15

If \(3 \\sin \\theta + 4 \\cos \\theta = 5\), then the value of \(3 \\cos \\theta - 4 \\sin \\theta\) is

A.0 B.1 C.5 D.-5

More for this chapter

About this Trigonometry test

This free online practice test covers Trigonometry from the 10th Standard Mathematics (Samacheer Kalvi) syllabus. Choose the number of questions and an optional time limit, then answer and submit — everything is checked in your browser, with the correct answers and a worked explanation shown at the end. For the full solutions to every question in this set, see the solved MCQs page.

More chapters in Mathematics

View all