Trigonometric Ratio

The word 'Trigonometry' is derived from Greek words 'tri', 'gon' and 'metron'. What does 'tri' mean?

In 'Trigonometry', what does 'gon' mean?

In 'Trigonometry', what does 'metron' mean?

Trigonometry is the study of relationship between—

Which civilization is believed to have made extensive use of trigonometry in land survey and engineering?

Early astrologers used trigonometry to determine—

At present, trigonometry is widely used in—

The naming of sides of a right-angled triangle is based on the position of—

The side of a right-angled triangle which is opposite to the right angle is called—

With respect to a given acute angle of a right triangle, the side directly opposite to that angle is called—

With respect to a given acute angle, the line segment that constitutes the angle along with the hypotenuse is called the—

In right-angled $\triangle PON$ (right angle at $N$), for $\angle PON$, $OP$ is the—

In right-angled $\triangle PON$ (right angle at $N$), for $\angle PON$, the adjacent side is—

In right-angled $\triangle PON$ (right angle at $N$), for $\angle PON$, the opposite side is—

In the same triangle, for $\angle OPN$, $OP$ is the—

For $\angle OPN$, the adjacent side is—

For $\angle OPN$, the opposite side is—

The hypotenuse of a right-angled triangle does not change with—

Which sides of a right triangle change names (opposite vs adjacent) depending on the chosen acute angle?

From Example 1(a), the right triangle has sides $17, 8, 15$. Hypotenuse is—

In Example 1(a), the opposite side of angle $\theta$ is—

Adjacent side in Example 1(a) is—

Which Greek letter is widely used to denote an angle?

The Greek letter 'phi' is written as—

In similar right-angled triangles, the ratios of sides corresponding to a fixed acute angle are—

The constancy of side ratios in $\triangle POM$ depends on—

The relation $\dfrac{PM}{OP} = \dfrac{P_1 M_1}{OP_1}$ expresses—

The three constant ratios of sides of $\triangle POM$ that depend only on the acute angle are called—

$\sin\theta = ?$

$\cos\theta = ?$

$\tan\theta = ?$

$\operatorname{cosec}\theta = ?$

$\sec\theta = ?$

$\cot\theta = ?$

$\operatorname{cosec}\theta = \dfrac{\text{hypotenuse}}{?}$

$\sec\theta = \dfrac{\text{hypotenuse}}{?}$

$\cot\theta = \dfrac{\text{adjacent}}{?}$

The symbol $\sin\theta$ means—

The symbol $\sin$ without an angle is—

How many trigonometric ratios are defined for an acute angle?

Which pair are reciprocals of each other?

$\sec\theta$ and which ratio are reciprocals?

The three primary trigonometric ratios are—

$\tan\theta = \dfrac{\sin\theta}{?}$

$\cot\theta = \dfrac{\cos\theta}{?}$

$\sin\theta \cdot \operatorname{cosec}\theta = ?$

$\cos\theta \cdot \sec\theta = ?$

$\tan\theta \cdot \cot\theta = ?$

$\sin^2\theta + \cos^2\theta = ?$

$1 + \tan^2\theta = ?$

$\sec^2\theta - \tan^2\theta = ?$

$\tan^2\theta = \sec^2\theta - ?$

$1 + \cot^2\theta = ?$

$\operatorname{cosec}^2\theta - \cot^2\theta = ?$

$\cot^2\theta = \operatorname{cosec}^2\theta - ?$

$1 - \sin^2\theta = ?$

$1 - \cos^2\theta = ?$

The Pythagorean theorem $\text{hyp}^2 = \text{opp}^2 + \text{adj}^2$ leads directly to which trigonometric identity?

For an integer index $n$, $\sin^n\theta$ means—

Which is NOT a Pythagorean trigonometric identity?

If $\tan A = \dfrac{4}{3}$, then opposite $:$ adjacent $= ?$

If $\tan A = \dfrac{4}{3}$, hypotenuse $= ?$

If $\tan A = \dfrac{4}{3}$, $\sin A = ?$

If $\tan A = \dfrac{4}{3}$, $\cos A = ?$

If $\tan A = \dfrac{4}{3}$, $\operatorname{cosec} A = ?$

If $\tan A = \dfrac{4}{3}$, $\sec A = ?$

If $\tan A = \dfrac{4}{3}$, $\cot A = ?$

In right $\triangle ABC$ with $\angle B = 90^\circ$, if $\tan A = 1$, then opposite and adjacent sides of $\angle A$ are—

If $\tan A = 1$, then $\sin A = ?$

If $\tan A = 1$, then $2\sin A \cos A = ?$

In right $\triangle ABC$ with $\angle C = 90^\circ$, $AB = 29$, $BC = 21$, $\angle ABC = \theta$. Then $AC = ?$

With the same data ($\angle C = 90^\circ$, $AB = 29$, $BC = 21$, $\angle ABC = \theta$), $\cos\theta = ?$

With the same data, $\sin\theta = ?$

With the same data, $\cos^2\theta - \sin^2\theta = ?$

If $\sin A = \dfrac{7}{25}$, $\cos A = ?$

If $15\cot A = 8$, then $\cot A = ?$

If $15\cot A = 8$, then opposite $:$ adjacent $= ?$

If $15\cot A = 8$, hypotenuse (taking opposite $= 15$, adjacent $= 8$) $= ?$

If $15\cot A = 8$, $\sin A = ?$

If $15\cot A = 8$, $\sec A = ?$

In right $\triangle ABC$ with $\angle C = 90^\circ$, $AB = 13$, $BC = 12$, $\angle ABC = \theta$. Then $AC = ?$

With $\angle C = 90^\circ$, $AB = 13$, $BC = 12$, the hypotenuse is—

In the same triangle, $\sin\theta = ?$

In the same triangle, $\cos\theta = ?$

In the same triangle, $\tan\theta = ?$

$\tan\theta + \cot\theta = ?$

$\sec^2\theta + \operatorname{cosec}^2\theta = ?$

$\dfrac{1}{1 + \sin^2\theta} + \dfrac{1}{1 + \operatorname{cosec}^2\theta} = ?$

$\dfrac{\tan A}{\sec A + 1} - \dfrac{\sec A - 1}{\tan A} = ?$

$\sqrt{\dfrac{1 - \sin A}{1 + \sin A}} = ?$

If $\tan A + \sin A = a$ and $\tan A - \sin A = b$, then $a^2 - b^2 = ?$

If $\sec A + \tan A = \dfrac{5}{2}$, then $\sec A - \tan A = ?$

$\dfrac{1 + \sin\theta}{\cos\theta} + \dfrac{\cos\theta}{1 + \sin\theta} = ?$

$\dfrac{\sin A}{\operatorname{cosec} A} + \dfrac{\cos A}{\sec A} = ?$

$\dfrac{\sec A}{\cos A} - \dfrac{\tan A}{\cot A} = ?$

$\dfrac{1}{1 + \tan^2 A} + \dfrac{1}{1 + \cot^2 A} = ?$

$\tan A \cdot \sqrt{1 - \sin^2 A} = ?$

$\dfrac{\sec A + \tan A}{\operatorname{cosec} A + \cot A} = ?$

$\dfrac{\operatorname{cosec} A}{\operatorname{cosec} A - 1} + \dfrac{\operatorname{cosec} A}{\operatorname{cosec} A + 1} = ?$

$\dfrac{1}{1 + \sin A} + \dfrac{1}{1 - \sin A} = ?$

$\dfrac{1}{\operatorname{cosec} A - 1} - \dfrac{1}{\operatorname{cosec} A + 1} = ?$

$\dfrac{\sin A}{1 - \cos A} + \dfrac{1 - \cos A}{\sin A} = ?$

$(\tan\theta + \sec\theta)^2 = ?$