alleryStart learning →cos(90°) equals:
- 1
- ∞
- 1/2
- 0
Show answer and solution
Correct answer: D. 0
cos(90°) = 0. (cos(0°) = 1, cos(180°) = -1.)
AMUEEE Sequences and Series — practice questions — page 2
Explore 136 free Sequences and Series questions in AMUEEE Mathematics. Open each question or exercise to read its content, reference answers and available explanation.
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cos(90°) equals:Read the answer and worked solution →sin²θ + cos²θ equals:Read the answer and worked solution →tan(45°) equals:Read the answer and worked solution →In which quadrant is sin θ positive and cos θ negative?Read the answer and worked solution →sec θ is defined as:Read the answer and worked solution →sin(A + B) equals:Read the answer and worked solution →cos(A + B) equals:Read the answer and worked solution →sin(60°) cos(30°) + cos(60°) sin(30°) equals:Read the answer and worked solution →If sin θ = 3/5 (θ in Q1), find cos θ:Read the answer and worked solution →Find cos(75°) using cos(A + B):Read the answer and worked solution →sin(2θ) equals:Read the answer and worked solution →Find sin(15°):Read the answer and worked solution →If tan θ = 1/2 (acute), find sin 2θ:Read the answer and worked solution →For 0 ≤ θ < 2π, solutions of sin θ = 1/2:Read the answer and worked solution →1 - cos²θ equals:Read the answer and worked solution →sin(A) + sin(B) equals (sum-to-product):Read the answer and worked solution →In a right triangle, if hypotenuse = 13 and one leg = 5, sin θ for angle θ opposite to that leg:Read the answer and worked solution →tan(A + B) equals:Read the answer and worked solution →sin(180° - θ) equals:Read the answer and worked solution →In triangle ABC with sides a, b, c opposite to angles A, B, C: sine rule states:Read the answer and worked solution →If sin θ + cos θ = 1, then sin θ × cos θ equals:Read the answer and worked solution →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 →
Worked practice questions
sin²θ + cos²θ equals:
- cos 2θ
- 2
- 0
- 1
Show answer and solution
Correct answer: D. 1
**Pythagorean identity:** sin²θ + cos²θ = 1 for all θ.
From right triangle x² + y² = r².
Sin = y/r, cos = x/r, so sin² + cos² = (x²+y²)/r² = 1.
tan(45°) equals:
- ∞
- 0
- 1
- √3
Show answer and solution
Correct answer: C. 1
We have tan(45°) = sin(45°)/cos(45°).
That is tan(45°) = (1/√2)/(1/√2).
So tan(45°) = 1.
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