Practice Quotient Identities (3.3) - Trigonometric Identities and Graphs

Practise this section

9 questions

Flashcard drill
3 cards from this section. Quick, good the night before a test.
Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
Sign up to start the exercise
Quiz
3 questions · about 2 min · pass mark 70%. Hints available.
Sign up to start the quiz

6 sample questions

Question 1.
What is tan(60°) using the quotient identity?
Show hintHide hint
Use known values of sin(60°) and cos(60°).
Question 2.
Express cot(30°) using the quotient identity.
Show hintHide hint
Remember the reciprocal relationship.
3Question 3.
What is the formula for tangent in terms of sine and cosine?
- tan(θ) = cos(θ)/sin(θ)
- tan(θ) = sin(θ)/cos(θ)
- tan(θ) = sin(θ) + cos(θ)
Show hintHide hint
Think about how tangent relates to the triangle ratios.
4Question 4.
True or False: Cotangent is equal to the reciprocal of tangent.
- True
- False
Show hintHide hint
Recall the definition of cotangent.
Question 5.
Prove that tan(θ) * cot(θ) = 1 using the quotient identities.
Show hintHide hint
Substituting the definitions of each function will reveal the identity.
Question 6.
Show how to derive the quotient identity for tangent using the unit circle approach.
Show hintHide hint
Refer to the coordinates of the unit circle where sine is the y-coordinate and cosine is the x-coordinate.

5 more questions in this section. Enroll free to practise them all.