Worksheet: Signs of Trigonometric Functions in Quadrants

In this worksheet, we will practice identifying in which quadrant an angle lies and whether its sine and cosine are positive or negative.

Q1:

Determine the quadrant in which 𝜃 lies if cos𝜃<0 and sin𝜃<0.

  • Athe third quadrant
  • Bthe second quadrant
  • Cthe fourth quadrant
  • Dthe first quadrant

Q2:

Determine the quadrant in which 𝜃 lies if cos𝜃>0 and sin𝜃<0.

  • Athe first quadrant
  • Bthe second quadrant
  • Cthe third quadrant
  • Dthe fourth quadrant

Q3:

In which quadrant does the angle 288 lie?

  • Afourth quadrant
  • Bthird quadrant
  • Csecond quadrant
  • Dfirst quadrant

Q4:

The angle 𝜃 is in standard position where sec𝜃<0. In which quadrants does the terminal side of 𝜃 lie?

  • Afirst or third
  • Bsecond or third
  • Cfirst or fourth
  • Dsecond or fourth

Q5:

Is csc(225) positive or negative?

  • Apositive
  • Bnegative

Q6:

Determine the quadrant in which 𝜃 lies if cos𝜃<0 and sin𝜃>0.

  • Athe first quadrant
  • Bthe fourth quadrant
  • Cthe second quadrant
  • Dthe third quadrant

Q7:

Is cos400 positive or negative?

  • Anegative
  • Bpositive

Q8:

In which quadrant does 𝜃 lie if sin𝜃=12 and cos𝜃=12?

  • Athe first
  • Bthe fourth
  • Cthe third
  • Dthe second

Q9:

Determine the quadrant in which 𝜃 lies if cos𝜃>0 and sin𝜃>0.

  • Athe second quadrant
  • Bthe third quadrant
  • Cthe fourth quadrant
  • Dthe first quadrant

Q10:

In which quadrant does 𝜃 lie if sin𝜃>0 and cos𝜃>0?

  • Afourth
  • Bsecond
  • Cthird
  • Dfirst

Q11:

Which of the following angles has a positive sine and a negative secant?

  • A 1 3 6 3 6
  • B 4 3 2 4
  • C 3 1 6 3 6
  • D 2 2 3 2 4

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