AimMent

For Class 8, 9 & 10

Foundation - a strong base in Physics, Chemistry, Maths & Biology

Concept-first questions with clear model answers across all four subjects, aligned to NCERT. Start early, build the habit, and walk into your board exams, NEET and JEE already ahead.

Class 824Class 924Class 1036
SubjectAllPhysics 19Chemistry 19Biology 19Mathematics 27
ChapterAllAcids, Bases and SaltsArithmetic ProgressionsCarbon and its CompoundsChemical Reactions and EquationsCirclesControl and CoordinationCoordinate GeometryElectricityHeredity and EvolutionHow do Organisms ReproduceIntroduction to TrigonometryLife ProcessesLight - Reflection and RefractionMagnetic Effects of Electric CurrentMetals and Non-metalsOur EnvironmentPair of Linear Equations in Two VariablesPolynomialsProbabilityQuadratic EquationsReal NumbersSome Applications of TrigonometryStatisticsSurface Areas and VolumesThe Human Eye and the Colourful WorldTriangles

Showing 2 questions for Class 10. Tap a card to reveal the answer.

MathematicsIntroduction to Trigonometrymedium

If sin(theta) = 3/5, find cos(theta) and tan(theta), where theta is acute.

Reveal answer ↓

What it is

The identity sin^2 + cos^2 = 1 lets you find one trig ratio from another for the same angle.

Answer

Using the identity sin^2(theta) + cos^2(theta) = 1, cos^2(theta) = 1 - (3/5)^2 = 1 - 9/25 = 16/25, so cos(theta) = 4/5 (positive since theta is acute). Then tan(theta) = sin/cos = (3/5) / (4/5) = 3/4.

sin^2(theta) + cos^2(theta) = 1 ; tan = sin/cos

  • •sin^2 + cos^2 = 1
  • •cos(theta) = 4/5
  • •tan(theta) = sin/cos = 3/4

Why learn this

Trig ratios drive navigation, physics waves, construction and computer graphics.

💡 Memory trick

Think of the 3-4-5 triangle: sin 3/5 -> cos 4/5 -> tan 3/4.

MathematicsIntroduction to Trigonometrymedium

Evaluate 2 tan^2(45 degrees) + cos^2(30 degrees) - sin^2(60 degrees).

Reveal answer ↓

What it is

The standard angles 0, 30, 45, 60 and 90 degrees have fixed trig values worth memorising.

Answer

Use standard values: tan(45 deg) = 1, cos(30 deg) = sqrt(3)/2, sin(60 deg) = sqrt(3)/2. So the expression = 2(1)^2 + (sqrt(3)/2)^2 - (sqrt(3)/2)^2 = 2 + 3/4 - 3/4 = 2.

tan45 = 1 ; cos30 = sqrt(3)/2 ; sin60 = sqrt(3)/2

  • •tan45 = 1, cos30 = sin60 = sqrt(3)/2
  • •2(1) + 3/4 - 3/4
  • •= 2

Why learn this

They appear in nearly every physics and maths problem - knowing them saves huge time.

💡 Memory trick

For sin, use sqrt(0..4)/2 across 0,30,45,60,90; cos is the same list reversed.