3G3 AMath - Trigo Ratios of angles in four quadrants

Trigo Ratios relating to angles in four quadrants

By Kangcheng Wang

Multiple Choice

In which quadrant does 225^o lie?

• 1st

• 2nd

• 3rd

• 4th

Multiple Choice

In which quadrant does 358^o lie?

• 1st

• 2nd

• 3rd

• 4th

Multiple Choice

In which quadrant does 94.9^o lie?

• 1st

• 2nd

• 3rd

• 4th

Multiple Choice

In which quadrant does −94.9^o lie?

• 1st

• 2nd

• 3rd

• 4th

Multiple Choice

In which quadrant does −301^o lie?

• 1st

• 2nd

• 3rd

• 4th

Multiple Choice

In which quadrant does −16^o lie?

• 1st

• 2nd

• 3rd

• 4th

​What is reference angle?

​For any given angle Θ, its reference angle, Θ^', is given in the diagram on the left.

E.g.,

If the given angle is 47^o then its reference angle is 47^o

If the given angle is 108^o then its reference angle is 180^o−108^o=72^o

​If 0^o<A<360^o, find the value of angle A for A is in the second quadrant and reference angle is 12.3^o.

​Step 1: Draw the diagram

Step 2: Red angle Θ' is the reference angle while Green angle Θ is the angle A

Step 3: Calculate angle A
180^o-12.3^o=167.7^o

​​What is reference angle?

Math Response

If 0<B<2π, find the value of B for B is in the first quadrant and reference angle is $$\frac{\pi}{6}$$ .

Type answer here

Correct Answer: \frac{\pi}{6}

Deg^°

Rad

Math Response

If 0<B<2π, find the value of B for B is in the second quadrant and reference angle is $$\frac{\pi}{5}$$ .

Type answer here

Correct Answer: \frac{4\pi}{5}

Deg^°

Rad

Math Response

If 0<B<2π, find the value of B for B is in the third quadrant and reference angle is $$\frac{2\pi}{9}$$ .

Type answer here

Correct Answer: \frac{11\pi}{9}

Deg^°

Rad

Math Response

If 0<B<2π, find the value of B for B is in the fourth quadrant and reference angle is $$\frac{3\pi}{11}$$ .

Type answer here

Correct Answer: \frac{19\pi}{11}

Deg^°

Rad

​Determine the possible quadrant angle lies

Given sinΘ > 0 and tanΘ > 0.

Which quadrant does Θ lie?

ANS:

Based on the diagram, angle Θ lies in the 1st quadrant.

Multiple Choice

Determine the possible quadrant in which angle Θ lies if cosΘ>0 and sinΘ<0.

• 1st

• 2nd

• 3rd

• 4th

Multiple Choice

Determine the possible quadrant in which angle Θ lies if tanΘ<0 and cosΘ<0.

• 1st

• 2nd

• 3rd

• 4th

Multiple Choice

Determine the possible quadrant in which angle Θ lies if sinΘ=4/5 and cosΘ>0.

• 1st

• 2nd

• 3rd

• 4th

Multiple Choice

Determine the possible quadrant in which angle Θ lies if cosΘ=-0.38 and tanΘ>0.

• 1st

• 2nd

• 3rd

• 4th

​Study Work Example 6 on pg211 of textbook and complete Practice Now 6 on foolscap