If sin θ = 12/13 (acute θ in Q1), find tan(θ/2):

A1/3

B3/4

C2/3

D1/5

Answer & Solution

Correct answer: C. 2/3

cos θ = √(1 − sin²θ) = √(1 − 144/169) = √(25/169) = 5/13 (positive in Q1). We have tan(θ/2) = (1 − cos θ)/sin θ. That is tan(θ/2) = (1 − 5/13)/(12/13). That is tan(θ/2) = (8/13)/(12/13). That is tan(θ/2) = 8/12. So tan(θ/2) = 2/3.

Practise this question with Quill — AP Calculus AB →

Keep practising Unit 3B: Implicit Differentiation and Inverse Functions

Browse all Unit 3B: Implicit Differentiation and Inverse Functions questions for AP Calculus AB, or explore more Mathematics topics.

Start a Unit 3B: Implicit Differentiation and Inverse Functions lesson →

Related questions

An event is described as having 'EVEN CHANCE'. Its probability is:If you toss a fair coin and the probability of heads is 1/2, what is the probability of NO The probability of drawing any number from 2 to 10 from a standard deck of 52 cards is:If a bag has 6 cards numbered 1 to 6, and 3 of them are purple, the probability of drawing The probability of an IMPOSSIBLE event is:Probability measures:Solve 3 ≤ 2x - 1 ≤ 7 (a DOUBLE inequality) for real x.Identify a QUADRATIC inequality (not a linear inequality).