Problems Based on Trigonometric Ratios

The video tutorial explains the basic definitions of trigonometric ratios: sine, cosine, and tangent, using the mnemonic 'Cartur'. It further discusses the reciprocal ratios: cosecant, secant, and cotangent. The tutorial highlights that the values of these ratios remain constant for a given angle, regardless of the triangle's side lengths. It also explains that the hypotenuse, being the longest side, results in sine and cosine values always being less than one, while secant and cosecant are greater than one. The video concludes with a discussion on trigonometric notations and the concept of triangle similarity based on equal trigonometric ratios.

What is the reciprocal of the sine function?

• Tangent

• Secant

• Cosecant

• Cotangent

Why are the values of sine and cosine always less than one?

• Because the opposite side is always longer than the hypotenuse

• Because the opposite side is always equal to the hypotenuse

• Because the hypotenuse is always the longest side

• Because the adjacent side is always longer than the hypotenuse

What happens to the values of secant and cosecant if the values of sine and cosine are always less than one?

• They are always zero

• They are always less than one

• They are always equal to one

• They are always greater than one

If the sine of angle B is equal to the sine of angle Q, what can be inferred about triangles ABC and PQR?

• They are similar

• They are congruent

• They are scalene

• They are isosceles

According to the isosceles triangle angle theorem, if cos A equals cos B, what can be said about angles A and B?

• Angles A and B are supplementary

• Angles A and B are different

• Angles A and B are equal

• Angles A and B are complementary