alleryStart learning →In which quadrant is sin θ positive and cos θ negative?
- III
- I
- IV
- II
Show answer and solution
Correct answer: D. II
Quadrant II (90° < θ < 180°): sin > 0, cos < 0, tan < 0. ASTC rule: All in I, Sin in II, Tan in III, Cos in IV (positive).
HPCET Probability & Statistics — practice questions — page 2
Explore 138 free Probability & Statistics questions in HPCET Mathematics. Open each question or exercise to read its content, reference answers and available explanation.
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Showing questions 31–60 of 138.
In which quadrant is sin θ positive and cos θ negative?Read the answer and worked solution →sin(A + B) equals:Read the answer and worked solution →If tan θ = 1/2 (acute), 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 →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 →Mode of data set is:Read the answer and worked solution →For random variable X uniform on [0, 1]: E(X²) =Read the answer and worked solution →E[X² + Y²] when X, Y are independent identically distributed with E(X) = 0, Var(X) = σ²:Read the answer and worked solution →At least one '6' in 4 throws of a fair die:Read the answer and worked solution →For two events A and B, P(A | B) = 0.6, P(B) = 0.5, P(A) = 0.4. P(B | A) =Read the answer and worked solution →Mean Absolute Deviation (MAD):Read the answer and worked solution →Two independent X, Y with Var(X) = 4, Var(Y) = 9. Var(X + Y) =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 →
Worked practice questions
sin(A + B) equals:
- cosA cosB - sinA sinB
- sinA cosB - cosA sinB
- sinA cosB + cosA sinB
- sinA + sinB
Show answer and solution
Correct answer: C. sinA cosB + cosA sinB
**Compound angle formula:** sin(A + B) = sinA cosB + cosA sinB.
(And sin(A - B) = sinA cosB - cosA sinB.)
If tan θ = 1/2 (acute), find sin 2θ:
- 1/5
- 3/5
- 4/5
- 2/5
Show answer and solution
Correct answer: C. 4/5
sin 2θ = 2 sinθ cosθ.
From tan = 1/2, draw right triangle: opp=1, adj=2, hyp=√5. sinθ = 1/√5, cosθ = 2/√5. So sin 2θ = 2(1/√5)(2/√5) = 4/5.
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