alleryStart learning →General solution of cos θ = 0:
- θ = π/2 + nπ
- θ = nπ
- θ = π/4 + nπ
- θ = 0 + 2nπ
Show answer and solution
Correct answer: A. θ = π/2 + nπ
cos θ = 0 at θ = π/2 and 3π/2 (i.e., 90° and 270°).
**General:** θ = π/2 + nπ where n ∈ ℤ. (Every π apart.)
CG PET Application of Integrals — practice questions — page 2
Explore 82 free Application of Integrals questions in CG PET Mathematics. Open each question or exercise to read its content, reference answers and available explanation.
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Showing questions 31–60 of 82.
General solution of cos θ = 0:Read the answer and worked solution →If tan θ + cot θ = 2, find sin 2θ:Read the answer and worked solution →If sin θ = 12/13 (acute θ in Q1), find tan(θ/2):Read the answer and worked solution →Minimum value of sin²θ + cos⁴θ:Read the answer and worked solution →If sin θ = 12/13 (acute), find tan(θ/2):Read the answer and worked solution →In triangle with sides 7, 8, 9, find cos of the angle opposite to side 9 (use cosine rule):Read the answer and worked solution →General solution of sin θ = sin α:Read the answer and worked solution →The arithmetic mean of n values x1, x2, ..., xn is:Read the answer and worked solution →Median of an odd-length sorted data set is:Read the answer and worked solution →Probability of a certain event:Read the answer and worked solution →Probability of rolling a 6 on a fair die:Read the answer and worked solution →For independent events A and B, P(A and B) equals:Read the answer and worked solution →Complete the arc length relationRead the answer and worked solution →Match each identity to its nameRead the answer and worked solution →The Pythagorean identitiesRead the answer and worked solution →Odd function or even function?Read the answer and worked solution →Complete the degree and radian conversionRead the answer and worked solution →True or false: identities and parityRead the answer and worked solution →Match each sum or difference formula to its resultRead the answer and worked solution →Signs in the expansionRead the answer and worked solution →Which formula does this belong to?Read the answer and worked solution →True or false: periodicityRead the answer and worked solution →Complete the complementary angle rulesRead the answer and worked solution →Assertion and reasonRead the answer and worked solution →Two are true, one is notRead the answer and worked solution →Three of these are wrong. Find the one that holds.Read the answer and worked solution →Order the steps: convert degrees to radiansRead the answer and worked solution →Flip and pair: identity with its valueRead the answer and worked solution →Spot the one that does not belongRead the answer and worked solution →Tap every correct identityRead the answer and worked solution →
Worked practice questions
If tan θ + cot θ = 2, find sin 2θ:
- 1/2
- 1
- 0
- 2
Show answer and solution
Correct answer: B. 1
We have tan θ + cot θ = sinθ/cosθ + cosθ/sinθ.
That is tan θ + cot θ = (sin²θ + cos²θ)/(sinθ cosθ).
That is tan θ + cot θ = 1/(sinθ cosθ).
So tan θ + cot θ = 2/sin(2θ).
We have **So 2/sin(2θ) = 2 → sin(2θ).
So **So 2/sin(2θ) = 1.**.
If sin θ = 12/13 (acute θ in Q1), find tan(θ/2):
- 1/3
- 3/4
- 2/3
- 1/5
Show answer and 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.
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