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.)
MP DTE Geometry — practice questions — page 2
Explore 134 free Geometry questions in MP DTE Mathematics. Open each question or exercise to read its content, reference answers and available explanation.
Practise Geometry with Quill →Geometry questions and exercises with answers
Showing questions 31–60 of 134.
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 →SAT · Mathematics · Trig Ratios (SOHCAHTOA)Read the answer and worked solution →SAT · Mathematics · Trig Identities — T/FRead the answer and worked solution →Match the trig identity to its resultRead the answer and worked solution →Complete the Identity: Trigonometry (ISC 12)Read the answer and worked solution →Match the trig valueRead the answer and worked solution →Fill the gaps in the triangle area ruleRead the answer and worked solution →Sort each inverse function into its domainRead the answer and worked solution →Tap every function whose domain is [−1, 1]Read the answer and worked solution →Match each inverse function to its domainRead the answer and worked solution →Match each inverse function to its principal value branchRead the answer and worked solution →Flip and pair: function with its principal rangeRead the answer and worked solution →Which principal ranges sit around zero, and which run 0 to π?Read the answer and worked solution →Tap every function whose principal range has a point removedRead the answer and worked solution →Name the principal value branchRead the answer and worked solution →Domain checkRead the answer and worked solution →Put the reasoning in order: why an inverse needs a restricted domainRead the answer and worked solution →True or false: existence of inversesRead the answer and worked solution →True or false: reading the tableRead 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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