Trigonometric Ratios

Math ⇒ Trigonometry

Trigonometric Ratios starts at 9 and continues till grade 12. QuestionsToday has an evolving set of questions to continuously challenge students so that their knowledge grows in Trigonometric Ratios. How you perform is determined by your score and the time you take. When you play a quiz, your answers are evaluated in concept instead of actual words and definitions used.

See sample questions for grade 11

Explain why tan 90° is undefined.

If sin θ = 0.6 and θ is in the second quadrant, what is the value of cos θ?

If \sin \theta = 0.8 and \theta is in the first quadrant, find \tan \theta.

If \sin \theta = \frac{3}{5} and \theta is in the first quadrant, find \cos \theta.

If \sin \theta = \frac{5}{13} and \theta is in the second quadrant, what is the value of \cos \theta?

If tan θ = 1, what are the possible values of θ between 0° and 360°?

If the adjacent side to angle \theta in a right triangle is 7 units and the hypotenuse is 25 units, find \cos \theta.

If the hypotenuse of a right triangle is 10 units and the side opposite to angle \theta is 6 units, find \sin \theta.

State the Pythagorean identity involving sin θ and cos θ.

State the relationship between sec θ and cos θ.

What is the value of sin 90°?

If \sec \theta = \frac{13}{5} and \theta is in the fourth quadrant, find the values of \sin \theta and \cos \theta.

If \sin \theta = -\frac{3}{5} and \theta is in the third quadrant, find the exact values of \cos \theta and \tan \theta.

If tan θ = -1 and θ is between 180° and 360°, what is the value of θ?

If the sides of a right triangle are in the ratio 5:12:13, what is the value of \tan \theta, where \theta is the angle opposite the side of length 5?

Prove that for any angle θ, sin²θ + cos²θ = 1 using the unit circle definition of trigonometric ratios.