Trigonometric Ratios and Quadrants

The video tutorial covers the process of drawing quadrants and setting up triangle problems to calculate trigonometric ratios like tan and cosec. It explains the impact of quadrant restrictions on angle calculations and explores multiple solutions for trigonometric ratios. The tutorial concludes with a graphical representation of the tangent function, highlighting its periodicity and behavior across different quadrants.

In which quadrant is the angle located if cos(x) is negative and the hypotenuse is positive?

• Fourth Quadrant

• Third Quadrant

• First Quadrant

• Second Quadrant

What is the correct ratio for tangent in a right triangle?

• Adjacent over Hypotenuse

• Hypotenuse over Opposite

• Opposite over Hypotenuse

• Opposite over Adjacent

What is the reciprocal of sine known as?

• Secant

• Tangent

• Cosecant

• Cotangent

Why is it important to consider the signs of the sides when calculating trigonometric ratios?

• To simplify calculations

• To determine the correct quadrant

• To ensure the triangle is right-angled

• To avoid incorrect ratio values

If there are no restrictions on the angle, what must be considered when determining trigonometric ratios?

• The angle is always in the fourth quadrant

• The angle is always in the first quadrant

• The angle could be in multiple quadrants

• The angle is always in the second quadrant

Which quadrant allows both sine and cosine to be positive?

• Third Quadrant

• Second Quadrant

• First Quadrant

• Fourth Quadrant

What happens to the sine value when the angle is in the fourth quadrant?

• Sine is undefined

• Sine is zero

• Sine is negative

• Sine is positive

If tan(θ) = 2, which quadrants could θ be located in?

• First and Third Quadrants

• First and Second Quadrants

• Second and Third Quadrants

• Third and Fourth Quadrants

What is the effect of moving a triangle to a different quadrant on its trigonometric ratios?

• Ratios change completely

• Ratios remain the same but signs may change

• Ratios and signs remain the same

• Ratios become undefined

How does the tangent function differ from sine and cosine in terms of periodicity?

• Tangent has a period of 360 degrees

• Tangent has a period of 270 degrees

• Tangent has a period of 180 degrees

• Tangent has a period of 90 degrees